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Question Solve for xx and yy in the linear equation 12y=8x−48312y = \frac{8x - 48}{3}.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation 12y=8x−48312y = \frac{8x - 48}{3}.
2. We need to solve for yy in terms of xx.

STEP 2

First, we will eliminate the fraction on the right side of the equation by multiplying both sides of the equation by the denominator of the fraction.
12y×3=(8x−483)×312y \times 3 = \left(\frac{8x - 48}{3}\right) \times 3

STEP 3

Perform the multiplication on both sides.
36y=8x−4836y = 8x - 48

STEP 4

Now, we need to solve for yy. To do this, we will divide both sides of the equation by 36 to isolate yy.
36y36=8x−4836\frac{36y}{36} = \frac{8x - 48}{36}

STEP 5

Simplify both sides of the equation.
y=8x36−4836y = \frac{8x}{36} - \frac{48}{36}

STEP 6

Reduce the fractions by dividing both the numerator and the denominator by their greatest common divisor.
y=8x36−4836y = \frac{8x}{36} - \frac{48}{36}
The greatest common divisor of 8 and 36 is 4, and for 48 and 36, it is 12.

STEP 7

Reduce the fractions to their simplest form.
y=8x4×9−4812×3y = \frac{8x}{4 \times 9} - \frac{48}{12 \times 3}

STEP 8

Complete the simplification.
y=2x9−43y = \frac{2x}{9} - \frac{4}{3}
This is the solution for yy in terms of xx.

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