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4x+2 (6x-2)=2x(5-2+6y)

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5 votes

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

User Andrew Bocz Jr
by
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