I need help with the following question.
Solve for y: 3x - 2y = 8 + x
Please show the steps and the answer, thanks.
3x - 2y = 8 + x
add -3x to both sides
-2y = 8 - 2x
divide both sides by -2
y = -4 + x
To solve for y in the equation 3x - 2y = 8 + x, we want to isolate the variable y on one side of the equation. Here is the step-by-step process:
Step 1: Combine like terms
Start by combining the x terms on both sides of the equation. Add -x to both sides to cancel out the x term on the right side of the equation:
3x - 2y - x = 8 + x - x
Simplifying further, we have:
2x - 2y = 8
Step 2: Move the -2y term to the other side
To isolate the y term, we need to move the -2y term to the right side of the equation. We can do this by adding 2y to both sides of the equation:
2x - 2y + 2y = 8 + 2y
This simplifies to:
2x = 8 + 2y
Step 3: Move the constant term to the other side
Now, we want to isolate the y term completely, so we move the constant term (8) to the left side of the equation. We can achieve this by subtracting 8 from both sides:
2x - 8 = 8 + 2y - 8
This simplifies to:
2x - 8 = 2y
Step 4: Divide by the coefficient of y
To solve for y, we divide both sides of the equation by 2:
(2x - 8) / 2 = 2y / 2
Simplifying:
x - 4 = y
Therefore, the solution for y is y = x - 4.
In summary, the steps to solve 3x - 2y = 8 + x for y are:
1. Combine like terms.
2. Move the -2y term to the other side.
3. Move the constant term to the other side.
4. Divide by the coefficient of y.
The final solution is y = x - 4.