Question

Solve the following system of equations to find x and y:
11x + 15y + 23 = 0
7x – 2y – 20 = 0

• A. x = 1, y = -1
• B. x = 1, y = 2
• C. x = 2, y = -3
• D. x = 3, y = -1

Answer 1

The correct option is C x = 2, y = -3

The given pair of equations are,

$11x+15y+23=0---\left(i\right)$
$7x-2y-20=0---\left(ii\right)$

From (ii),

$2y=7x-20$
$y=\frac{7x-20}{2}---\left(iii\right)$

Now substituting y in (i),
$\Rightarrow 11x+15\left(\frac{7x-20}{2}\right)+23=0$

$\Rightarrow 11x+\left(\frac{105x-300}{2}\right)+23=0$

$\Rightarrow 22x+105x-300+46=0$

$\Rightarrow 127x-254=0$

$\Rightarrow x=2$

Next, putting the value of x in (iii).

$\Rightarrow y=\frac{7\times 2-20}{2}$

$\therefore y=-3$

Thus the value of x and y found to be 2 and -3 respectively.