Question

Which ordered pair is a solution to the system of equations?

{2x−y=−12x−4y=8


(8, 2)

(7, −5)

(−2, −3)

(1, 3)

Answer 1

When you share system of equations, please be sure to separate them (e. g., with a comma, a semicolon,  several spaces, or by putting one equation only on each line.  I prefer that

{2x−y=−12x−4y=8   be shared as

2x−y=−12
x−4y=8

Solving the 2nd for x:  x = 4y+8.  Sub 4y+8 for x in the first equation:

2(4y+8) - y = -12.  Multiplying as indicated, 8y + 16 - y = -12.

Consolidating the y terms, 7y = - 28, and y = -4
.  
Subst. -4 for y in x=4y+8, obtaining x = -16+8, or x = -8.
 


The proposed solution is (-8,-4).  You should definitely check this solution by subbing -8 for x and -4 for y in one of the original equations.