Question

Use elimination to solve the system of equations. Find the ordered pairs.

{ 1/2x+y=4
-2x-2y=-6

Answer 1

ok so the first thing you gotta do is to make sure you label your equations as one and two. Then you have two variables that will eliminate each other. In this case you can do that.

Answer 2

1/2x + y = 4 (1) x 2
-2x - 2y = -6

you are multiplying the first equation by 2 to get the same coefficient like the 2nd equation. Not necessarily the same sign (positive and negative)

Answer 3

after multiplying your equations will be

x + 2y = 8 (1)
-2x - 2y = -6 (2)

Now you can either subtract or add depending on how you wanna eliminate the targeted variable. So for this one, you can add cuz the coefficients have opposite signs.

x + 2y = 8
+
-2x - 2y = - 6
-----------------
-x(-1) = 2(-1)
x = -2


Now find what y is equal to, use your original equations, you can use either ones.

1/2x + y = 4 (1)
1/2(-2) + y = 4
-1 + y = 4
y = 4 + 1
y = 5

Therefore the solution to the system of equations is: ( -2, 5)

Answer 4

thank you so much for explaining it out! <3

Answer 5

aha it took a while :$
sorry about that :P