Question

Using elimination, the equations 3x - 4y = 12 and x + 4y = 20 can be solved to show that x = 8 and y = 3. Is this true or false ?

Answer 1

Both equations have a 4y term, so we can use elimination to easily solve the system.

3x - 4y = 12
x + 4y = 20
----------------
4x + 0y = 32

Now we can solve for x.

4x = 32

x = 8

Now we plug 8 in for x in either of the original equations to find y.

3(8) - 4y = 12

24 - 4y = 12

-4y = -12

y = 3

So yes, it is true that x = 8 and y = 3.

Hope this helps :)

Answer 2

3x - 4y = 12 ----- (1)
x + 4y = 20 ------ (2)

equation (2) x 3:
3x + 12y = 60 ---(2a)

(2a) - (1):
12y - (-4y) = 60 - 12
12y + 4y = 48
16y = 48
y = 3 ---- sub into equation (2)

x + 4(3) = 20
x + 12 = 20
x = 8

Ans: x = 8 and y = 3 (True)