We are asked to solve the system by the elimination method:
x - y = 4
2 x – 4 y = 20
So, we decide to try to eliminate the term in "x" by making sure that the x term in the first equation is exactly the OPPOSITE of the term in x in the second equation. For that we need in the first equation to read "- 2 x"as the x term. Then, we have to multiply the first equation by the factor "- 2" as shown below:
(-2) ( x - y ) = (-2) 4
-2 x + 2 y = - 8
now we combine term by term this new form of the first equation with the second equation given:
-2 x + 2 y = - 8
2 x – 4 y= 20
____________
0 + 2 y - 4 y = 20 - 8
- 2 y = 12
divide both sides by (-2) to isolate y com[;etely
y = 12 / (-2)
y = - 6
Now we use this value we found for y in the original first equation to solve for x:
x - y = 4
x - (-6) = 4
x + 6 = 4
suntract 6 from both sides to isolate x on the left
x = 4 - 6
x = -2
Then the answer to the system is x = -2 and y = - 6 which makes the following coordinate pair: (-2, -6)