Answer:
Slope intercept: y = (-1/3)x + (5/6)
or
x and y : x= 1/2 and y= 1/6
Explanation:
Firstly, distribute the 2 on the left side of the equals
4x+12x-4 = 2x(5-2+6y)
Then, distribute the 2x on the right side of the equals
4x+12x-4 = 10x-4x+12xy
Next, add like terms on both sides
16x-4 = 6x+12xy
Then, subtract 6x to move it to the left
10x-4 = 12xy
Next, divide by 12x to isolate the variable y
y = (10x-4) / 12x
simplify the right side
y = (5/6) - (1/3)x
if you need this in slope intercept form this is your answer
y = (-1/3)x + (5/6)
if you need the answers to all variables then we take our original equation and plug what we got for y in to all the spots that have the variable y
4x + 2 (6x-2) = 2x (5-2+6((-1/3)x+(5/6))
then we distribute once more
4x+12x-4 = -4x^2 + 16x
then we combine like terms
16x - 4 = -4x^2 + 16x
subract 16x from the right
-4 = -4x^2
square root the left
-2 = -4x
divide by -4
x = 1/2
now we can take this and plug it into our original equation to get the answer of y
4(1/2) + 2(6(1/2)-2) = 2(1/2)(5-2+6y)
evaluate
2 + 2 = 5 - 2 + 6y
4 = 3 + 6y
1 = 6y
y = 1/6