Question

Solvw the following pair of linear equations:

$2x+5y=13$ and $4x-9y=7$

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

Answer 1

The correct option is D $(4,1)$

$2x+5y=13$ ......$\left(1\right)$

$4x-9y=7$ ....$\left(2\right)$

Multiplying equation $\left(1\right)$ by $4$. we get,

$8x+20y=52$ ....(3)

Now, Multiplying equation $\left(2\right)$ by $2$. we get,

$8x-18y=14$ ......$\left(4\right)$

On subtracting $\left(4\right)$ from $\left(3\right)$. we get,

$38y=38\Rightarrow y=1$

On substitute the value of $y=1$ in $\left(1\right)$. we get,

$2x+5\left(1\right)=13\Rightarrow 2x=8\Rightarrow x=4$

Thus solution of given equations is $(4,1)$

Option D is correct.