Math Ch 3: Pair of Linear Equations in Two Variables PYQs | CBSE Class 10

Assertion (A): The value of $p$ for which the system of equations $4x+py+8=0$ and $x+2y+2=0$ 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 marks]

Solve the following system of equations for $x$ and $y$ :

$\frac{x}{2}+\frac{2y}{3}=-1$ and $x-\frac{y}{3}=3$

[2 marks]

(a) Solve the following system of equations graphically:

$x+3y=6$; $2x-3y=12$

OR

(b) x and y are complementary angles such that $x:y=1:2$. Express the given information as a system of linear equations in two variables and hence solve it.

[3 marks]

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 mark]

(A) Solve the following pair of linear equations for $x$ and $y$ algebraically :
$x+2y=9$ and $y-2x=2$

OR

(B) Check whether the point $(-4,3)$ lies on both the lines represented by the linear equations $x+y+1=0$ and $x-y=1$.

[2 marks]

The greater of two supplementary angles exceeds the smaller by $18^{\circ}$. Find measures of these two angles.

[3 marks]

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

[1 mark]

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 mark]

(a) Solve for x and y: \( x+y=6 \), \( 2x-3y=4 \).

OR

(b) Find out whether the following pair of linear equations are consistent or inconsistent:
\( 5x-3y=11 \)
\( -10x+6y=22 \)

[2 marks]