Question

Solve the following system of equations. 9x+8y=-3 5x-2y=-21

Answer 1

Solving with substitution:

1. Express $x$ from first equation:
$9x+8y=-3$
$9x=-3-8y$
$x=\frac{-3-8y}{9}=-\frac{3+8y}{9}$

2. Replace $x$ in second equation with found value and solve it:
$5(-\frac{3+8y}{9})-2y=-21$
$-\frac{15+40y}{9}-2y=-21$
$-\frac{15+40y}{9}-\frac{18y}{9}=-21$
$\frac{15+40y}{9}+\frac{18y}{9}=21$
$\frac{15+40y+18y}{9}=21$
$\frac{15+58y}{9}=21$
$15+58y=21*9$
$58y=189-15$
$58y=174$
$y=\frac{174}{58}=3$

3. Replace $y$ in first equation with found value and solve it:
$9x+8*3=-3$
$9x+24=-3$
$9x=-3-24$
$9x=-27$
$x=\frac{-27}{3}=-9$

So, $x=-9$ and $y=3$

Answer 2

9x+8y=-3
5x-2y=-21

multiply 2nd equation by 4
9x + 8y  = -3
20x - 8y = -84
-----------------add
29x = -87
x = -3

9x+8y=-3
9(-3)+8y=-3
-27 + 8y = -3
8y = -3 +27
8y = 24
y = 3

answer
(-3,3)