Question

State true\false:

$3x+2y=5,2x-3y=7$ is an example of consistent pair of equations.

• A. True
• B. False

Answer 1

The correct option is A True

Let $3x+2y=5$ ......(1)
and $2x-3y=7$ ......(2)
Multiply equation (1) by $2$ and equation (2) by $3$

Therefore, $6x+4y=10$ ....(3)

and $6x-9y=21$ ....(4)

Subtract equations (3) and (4), we get

$\Rightarrow 13y=-11$
$\Rightarrow y=-\frac{11}{13}$
Substitute the value of $y$ in $\left(1\right)$
$\Rightarrow 3x+2(-\frac{11}{13})=5$
$\Rightarrow 3x-\frac{22}{13}=5$
$\Rightarrow 3x=\frac{87}{13}$
$\Rightarrow x=\frac{29}{13}$
$\therefore x=\frac{29}{13},y=-\frac{11}{13}$
Hence, the pair of equations are consistent.
The correct answer is $A$.