Question

Solve the following
$3x-4y=25$
$-2x+y=-10$

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

Answer 1

Answer: (A)

$(3,-4)$

Consider the equations:

$3x-4y=25...\left(1\right)$

$-2x+y=-10...\left(2\right)$

Multiply equation $\left(2\right)$ by $4$, we get

$-2x\left(4\right)+y\left(4\right)=-10\left(4\right)$

$\Rightarrow$ $-8x+4y=-40...\left(3\right)$

Now add equation $\left(1\right)$ and $\left(3\right)$, we get

$3x-8x-4y+4y=25-40$

$\Rightarrow$$-5x=-15$

$\Rightarrow$$x=3$

Substitute $x=3$ in equation $\left(2\right)$

$-2\left(3\right)+y=-10$

$\Rightarrow$$-6+y=-10$

$\Rightarrow$$-y=-10+6$

$\Rightarrow$$-y=-4$

Hence, $x=3$ and $y=-4$