Answer/Step-by-step explanation:
These equations are set up to solve using the method called Substitution.
The second equation:
x = -2y + 12
is already set equal to x. So we can see that x is exactly -2y+12. So we are going to stuff -2y+12 in place of x in the first equation.
1st eq: 6x - 4y = 8
replace x with -2y+12.
Like this:
6(-2y+12) - 4y = 8
use distributive property
-12y + 72 - 4y = 8
combine like terms
-16y + 72 = 8
subtract 72 from both sides
-16y = -64
divide both sides by -16
y = 4
Now use y=4 in either equation (or both to do a check) to find x.
x = -2y + 12
x = -2(4) + 12
x = -8 + 12
x = 4
So, x = 4 and y = 4, we can write this as (4,4)
To check we can do the calculation for x in the other equation:
6x - 4y = 8
6x - 4(4) = 8
6x - 16 = 8
Add 16
6x = 24
Divide by 6
x = 4
check!
The solution is (4,4)