Question

Solve the system using the addition method.
–5x – 9y = 28
–4x + 5y = –2

A. (–2, –2)
B. (7, –4)
C. (7, 6)
D. (–11, 3)

Answer 1

Answer:

Option A

Step-by-step explanation:

–5x – 9y = 28    Equation 1

–4x + 5y = –2    Equation 2

We to eliminate one of the variables. In this case "Y" by using the appropiate number, in this case $\frac{9}{5}$

–5x – 9y = 28

$\frac{9}{5}$*{–4x + 5y = –2  

We have:

–5x – 9y = 28

$\frac{-36}{5}X +9Y=-\frac{18}{5}$

We have:

–5x = 28

$\frac{-36}{5}X =-\frac{18}{5}$

So, We have:

$\frac{-36}{5}X -5X=-\frac{18}{5}+28$

-61X= 122

$X=-\frac{122}{61}=-2$

Using Equation 2. We have:

-4*(-2)+5Y=-2

8+5Y=-2

5Y=-10

Y=$\frac{-10}{5} =-2$

Finally:

X=-2

Y=-2