Pair of Linear Equations in Two Variables: 1 mark Questions (CBSE Class 10)

If a pair of linear equations in two variables is represented by two coincident lines, then the pair of equations has :

1. (A)a unique solution
2. (B)two solutions
3. (C)no solution
4. (D)an infinite number of solutions

If the pair of linear equations : $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ is consistent and dependent, then

1. (A)$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
2. (B)$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}=\frac{c_1}{c_2}$
3. (C)$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
4. (D)$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

The pair of linear equations $\frac{3x}{2}+\frac{5y}{3}=7$ and $9x+10y=14$, is :

1. (A)consistent
2. (B)inconsistent
3. (C)consistent with one solution
4. (D)consistent with many solutions

Equation of another line parallel to the line represented by $2x-6y=7$ is :

1. (A)$y=3x-7$
2. (B)$2x=9-6y$
3. (C)$x-3y=7$
4. (D)$x=\frac{7}{2}-3y$

Equation of a line coincident with $2.5x-2y=3$ is :

1. (A)$5x-4y=3$
2. (B)$5x-4y+6=0$
3. (C)$15x-12y-3=0$
4. (D)$5x-4y-6=0$

The value of k for which the system of linear equations $\frac{x}{2}+\frac{y}{3}=5$ and $2x+ky=7$ is inconsistent, is

1. (A)$\frac{3}{4}$
2. (B)$\frac{4}{3}$
3. (C)$\frac{1}{3}$
4. (D)3

The value of k for which the system of linear equations $kx-y-2=0$ and $6x-2y-3=0$ has infinitely many solutions, is (does)

1. (A)$\frac{1}{2}$
2. (B)3
3. (C)4
4. (D)Not exist

Assertion (A): The system of linear equations $3x-5y+7=0$ and $-6x+10y+14=0$ is inconsistent.
Reason (R): When two linear equations don’t have unique solution, they always represent parallel lines.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

Assertion (A) : The value of p for which the system of equations $4x+py+8=0$ and $2x+2y+2=0$ is consistent is 4.
Reason (R) : The system of equations $a_{1}x+b_{1}y=c_1$ and $a_{2}x+b_{2}y=c_2$ is consistent with infinitely many solutions, if $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

If (0, 0) is the solution of the equation $x+y=c-1$, then the value of $c$ is :

1. (A)$0$
2. (B)$1$
3. (C)$-1$
4. (D)any real number

The number of solutions of the system of equations $x=3$, $y=-1$ is :

1. (A)$0$
2. (B)$1$
3. (C)$2$
4. (D)Infinite

The number of solutions of the system of equations $x=a$, $x=b$ $(a\ne b)$ is :

1. (A)$0$
2. (B)$1$
3. (C)$2$
4. (D)Infinite

For what value(s) of $k$ does the system of equations $kx+2y=3$ and $2x+y=5$ have a unique solution ?

1. (A)$k$ = a real number
2. (B)$k\ne 8$
3. (C)$k\ne 4$
4. (D)$k=4$

For what value(s) of $k$, is the system of equations $kx+2y=3$ and $2x+y=5$ inconsistent ?

1. (A)$k$ = Any real number
2. (B)$k\ne 2$
3. (C)$k\ne 4$
4. (D)$k=4$

The system of linear equations given by $x=a$ and $y=b$ is :

1. (A)Consistent with a unique solution.
2. (B)Consistent with infinitely many solutions.
3. (C)Consistent with two solutions.
4. (D)Inconsistent.

The value of $m$ for which lines $14x+my=20$ and $-3x+2y=16$ are parallel, is :

1. (A)$-\frac{3}{14}$
2. (B)$-\frac{7}{3}$
3. (C)$-\frac{28}{3}$
4. (D)$-\frac{3}{28}$

The line $2x-3y=6$ intersects $x$ – axis at

1. (A)(0, $-2$)
2. (B)(0, 3)
3. (C)($-2$, 0)
4. (D)(3, 0)

The value of k for which the system of equations $3x-7y=1$ and $kx+14y=6$ is inconsistent, is

1. (A)$-6$
2. (B)$\frac{2}{3}$
3. (C)6
4. (D)$\frac{-3}{2}$

The point (3, $-$ 5) lies on the line $mx-y=11$. The value of m is

1. (A)3
2. (B)$-2$
3. (C)8
4. (D)2

If $x=1$ and $y=2$ is a solution of the pair of linear equations $2x-3y+a=0$ and $2x+3y-b=0$, then :

1. (A)$a=2b$
2. (B)$2a=b$
3. (C)$a+2b=0$
4. (D)$2a+b=0$

The line represented by the equation $x-y=0$ is :

1. (A)parallel to x-axis
2. (B)parallel to y-axis
3. (C)passing through the origin
4. (D)passing through the point $(3,2)$

The equation of a line parallel to the x-axis and at a distance of 3 units below x-axis is :

1. (A)$x=3$
2. (B)$x=-3$
3. (C)$y=-3$
4. (D)$y=3$

Assertion (A) : The pair of linear equations $px+3y+59=0$ and $2x+6y+118=0$ will have infinitely many solutions if $p=1$.
Reason (R) : If the pair of linear equations $px+3y+19=0$ and $2x+6y+157=0$ has a unique solution, then $p\ne 1$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

The equation of a line parallel to y-axis and at a distance of 5 units to the right of y-axis is :

1. (A)$x=5$
2. (B)$x=-5$
3. (C)$y=5$
4. (D)$y=-5$

The value of 'k' for which the system of linear equations $6x+y=3k$ and $36x+6y=3$ have infinitely many solutions is :

1. (A)6
2. (B)$\frac{1}{6}$
3. (C)$\frac{1}{2}$
4. (D)$\frac{1}{3}$

A system of two linear equations in two variables is inconsistent, if the lines in the graph are :

1. (A)coincident
2. (B)parallel
3. (C)intersecting at one point
4. (D)intersecting at right angles

The value of '$p$' for which the equations $px+3y=p-3$, $12x+py=p$ has infinitely many solutions is :

1. (A)$-6$ only
2. (B)$6$ only
3. (C)$\pm 6$
4. (D)Any real number except $\pm 6$

The system of equations $2x+1=0$ and $3y-5=0$ has

1. (A)unique solution
2. (B)two solutions
3. (C)no solution
4. (D)infinite number of solutions

The system of equations $x+5=0$ and $2x-1=0$, has

1. (A)No solution
2. (B)Unique solution
3. (C)Two solutions
4. (D)Infinite solutions

The system of equations $y+a=0$ and $2x=b$ has

1. (A)No solution
2. (B)$\left(-a,\frac{b}{2}\right)$ as its solution
3. (C)$\left(\frac{b}{2},-a\right)$ as its solution
4. (D)Infinite solutions

The value of $k$ for which the pair of linear equations $5x+2y-7=0$ and $2x+ky+1=0$ don't have a solution, is :

1. (A)5
2. (B)$\frac{4}{5}$
3. (C)$\frac{5}{4}$
4. (D)$\frac{5}{2}$

The value of ‘k’ for which the pair of linear equations $x+y-4=0$ and $2x+ky-8=0$ has infinitely many solutions, is

1. (A)$k\ne 2$
2. (B)$k\ne -2$
3. (C)$k=2$
4. (D)$k=-2$

The graph of a pair of linear equations $a_{1}x+b_{1}y=c_1$ and $a_{2}x+b_{2}y=c_2$ in two variables $x$ and y represents parallel lines, if

1. (A)$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
2. (B)$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
3. (C)$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}=\frac{c_1}{c_2}$
4. (D)$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

The value of ‘p’ for which the pair of equations $-2x+3y-9=0$ and $4x+py+7=0$ has a unique solution is

1. (A)$p\ne 6$
2. (B)$p=6$
3. (C)$p=-6$
4. (D)$p\ne -6$

The lines represented by linear equations $x=a$ and $y=b$ $(a\ne b)$ are

1. (A)intersecting at (a, b).
2. (B)intersecting at (b, a).
3. (C)parallel.
4. (D)coincident.

Assertion (A): The pair of linear equations $5x+2y+6=0$ and $7x+6y+18=0$ have infinitely many solutions.
Reason (R): The pair of linear equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ have infinitely many solutions, if $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

The pair of linear equations $2kx+5y=7$, $6x+5y=11$ have a unique solution, if

1. (A)$k\ne 3$
2. (B)$k\ne -3$
3. (C)$k\ne \frac{1}{3}$
4. (D)$k\ne -\frac{1}{3}$

In the given figure, graphs of two linear equations are shown. The pair of these linear equations is :

1. (A)consistent with unique solution.
2. (B)consistent with infinitely many solutions.
3. (C)inconsistent.
4. (D)inconsistent but can be made consistent by extending these lines.

The value of k for which the system of equations $3x-y+8=0$ and $6x-ky+16=0$ has infinitely many solutions, is

1. (A)$-2$
2. (B)2
3. (C)$\frac{1}{2}$
4. (D)$-\frac{1}{2}$

The pair of linear equations $x+2y+5=0$ and $-3x=6y-1$ has

1. (A)unique solution
2. (B)exactly two solutions
3. (C)infinitely many solutions
4. (D)no solution

If a pair of linear equations in two variables is consistent, then the lines represented by the two equations are :

1. (A)always intersecting
2. (B)parallel
3. (C)always coincident
4. (D)intersecting or coincident

If $ax+by=a^2-b^2$ and $bx+ay=0$, then the value of $x+y$ is :

1. (A)$a^2-b^2$
2. (B)$a+b$
3. (C)$a-b$
4. (D)$a^2+b^2$

Two lines are given to be parallel. The equation of one of these lines is $5x-3y=2$. The equation of the second line can be :

1. (A)$-15x-9y=5$
2. (B)$15x+9y=5$
3. (C)$9x-15y=6$
4. (D)$-15x+9y=5$

The pair of linear equations y = 0 and y = $-7$ have

1. (A)exactly one solution
2. (B)two solutions
3. (C)infinitely many solutions
4. (D)no solution

Which out of the following type of straight lines will be represented by the system of equations $3x+4y=5$ and $6x+8y=7$ ?

1. (A)Parallel
2. (B)Intersecting
3. (C)Coincident
4. (D)Perpendicular to each other

The larger of two supplementary angles exceeds the smaller by 18 degrees. What is the measure of larger angle ?

1. (A)$81^{\circ }$
2. (B)$99^{\circ }$
3. (C)$36^{\circ }$
4. (D)$54^{\circ }$

Assertion (A) : The system of linear equations $3x+5y-4=0$ and $15x+25y-25=0$ is inconsistent.
Reason (R) : The pair of linear equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ is inconsistent if $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

The pair of linear equations $x+2y-5=0$ and $2x-4y+6=0$ :

1. (A)is inconsistent
2. (B)is consistent with many solutions
3. (C)is consistent with a unique solution
4. (D)is consistent with two solutions

The lines represented by the linear equations $y=x$ and $x=4$ intersect at P. The coordinates of the point P are :

1. (A)(4, 0)
2. (B)(4, 4)
3. (C)(0, 4)
4. (D)$(-4,4)$

The pair of linear equations $x+2y+5=0$ and $-3x-6y+1=0$ has :

1. (A)a unique solution
2. (B)exactly two solutions
3. (C)infinitely many solutions
4. (D)no solution

If the pair of linear equations $x-y=1$, $x+ky=5$ has a unique solution $x=2$, $y=1$, then the value of $k$ is :

1. (A)$-2$
2. (B)$-3$
3. (C)3
4. (D)4

The value of k for which the equations $3x-y+8=0$ and $6x-ky+16=0$ represent coincident lines is :

1. (A)$\frac{1}{2}$
2. (B)$-\frac{1}{2}$
3. (C)2
4. (D)$-2$

If the lines represented by equations $3x+2my=2$ and $2x+5y+1=0$ are parallel, then the value of m is :

1. (A)$\frac{2}{5}$
2. (B)$-\frac{5}{4}$
3. (C)$\frac{3}{2}$
4. (D)$\frac{15}{4}$

The value of k, if (6, k) lies on the line represented by $x-3y+6=0$, is

1. (A)$-4$
2. (B)12
3. (C)$-12$
4. (D)4

The value of ‘k’ for which the system of equations $kx+2y=5$ and $3x+4y=1$ have no solution, is

1. (A)$k=\frac{3}{2}$
2. (B)$k\ne \frac{3}{2}$
3. (C)$k\ne \frac{2}{3}$
4. (D)$k=15$

The value of ‘p’ if (–2, p) lies on the line represented by the equation $2x-3y+7=0$, is

1. (A)$-\frac{13}{2}$
2. (B)$\frac{13}{2}$
3. (C)$-1$
4. (D)1

The value of k for which the pair of equations $kx=y+2$ and $6x=2y+3$ has infinitely many solutions,

1. (A)is k = 3
2. (B)does not exist
3. (C)is k = –3
4. (D)is k = 4

If the pair of equations $3x-y+8=0$ and $6x-ry+16=0$ represent coincident lines, then the value of ‘r’ is :

1. (A)$-\frac{1}{2}$
2. (B)$\frac{1}{2}$
3. (C)$-2$
4. (D)$2$

The pair of equations $x=a$ and $y=b$ graphically represents lines which are :

1. (A)parallel
2. (B)intersecting at (b, a)
3. (C)coincident
4. (D)intersecting at (a, b)

If $2x+3y=15$ and $3x+2y=25$, then the value of $x-y$ is :

1. (A)$-10$
2. (B)8
3. (C)10
4. (D)$-8$

The pair of linear equations $2x=5y+6$ and $15y=6x-18$ represents two lines which are :

1. (A)intersecting
2. (B)parallel
3. (C)coincident
4. (D)either intersecting or parallel

The pair of equations $ax+2y=9$ and $3x+by=18$ represent parallel lines, where a, b are integers, if :

1. (A)$a=b$
2. (B)$3a=2b$
3. (C)$2a=3b$
4. (D)$ab=6$

The solution of the pair of equations $x+y=a+b$ and $ax-by=a^2-b^2$ is :

1. (A)x = b, y = a
2. (B)x = $-a$, y = b
3. (C)x = a, y = b
4. (D)x = a, y = $-b$

The point of intersection of the line represented by $3x-y=3$ and y-axis is given by

1. (A)(0, –3)
2. (B)(0, 3)
3. (C)(2, 0)
4. (D)(–2, 0)

3 chairs and 1 table cost ₹ 900; whereas 5 chairs and 3 tables cost ₹ 2,100. If the cost of 1 chair is ₹ x and the cost of 1 table is ₹ y, then the situation can be represented algebraically as

1. (A)$3x+y=900$, $3x+5y=2100$
2. (B)$x+3y=900$, $3x+5y=2100$
3. (C)$3x+y=900$, $5x+3y=2100$
4. (D)$x+3y=900$, $5x+3y=2100$

The coordinates of the point where the line $2y=4x+5$ crosses $x$-axis is

1. (A)$\left(0,\frac{-5}{4}\right)$
2. (B)$\left(0,\frac{5}{2}\right)$
3. (C)$\left(\frac{-5}{4},0\right)$
4. (D)$\left(\frac{-5}{2},0\right)$

The point of intersection of the line represented by $3x-y=3$ and the y-axis is given by

1. (A)(0, –3)
2. (B)(0, 3)
3. (C)(2, 0)
4. (D)(–2, 0)

The condition for the system of linear equations $ax+by=c$; $lx+my=n$ to have a unique solution is

1. (A)$am\ne bl$
2. (B)$al\ne bm$
3. (C)$al=bm$
4. (D)$am=bl$