The document provides step-by-step instructions for solving equations for a variable by isolating it on one side of the equation. It demonstrates the process for a variety of equations, showing how to move all other terms to the other side by taking their opposite and then dividing both sides by the coefficient of the variable. The goal is to isolate the variable y on one side of the equation with any numbers or other variables on the other side.

1. Solving For Y Created by Mrs. Ulshafer March 14, 2010

2. Solve each equation for y y – 2x = 1 +2x + 2x y = 2x + 1 Leave the y (in red), move everything else Opposite of -2x is +2x Can't combine +2x & 1 (not like terms) Since the y is positive with no other numbers in front you are done.

3. Solve each equation for y 3x + y = 3 -3x -3x y = -3x + 3 Leave the y (in red), move everything else Opposite of 3x is -3x Can't combine -3x & 3 (not like terms) y is alone and positive, nothing left to do

4. Solve each equation for y 4x + 2y = 1 -4x -4x + 2y = -4x + 1 2 2 2 y = -2x + 1/2 Leave the y (in red), move everything else Opposite of +4x is -4x Can't combine -4x & 1 (not like terms) Opposite of 2 times y, is division Simplify as much as possible. (No decimals, leave as fractions)

6. Solve each equation for y 2x + 3y = 10 -2x -2x 3y = -2x + 10 /3 /3 /3 y = -2x/3 + 10/3 Leave the y (in red), move everything else Opposite of +2x is -2x Can't combine -2x & 10 (not like terms) Opposite of 3 times y, is divide Simplify as much as possible. (No decimals, leave as fractions)

7. Solve each equation for y 2y – 4x = 6 +4x +4x 2y = 4x + 6 /2 /2 /2 y = 2x + 3 Leave the y (in red), move everything else Opposite of -4x is +4x Can't combine 4x & 6 (not like terms) Opposite of 2 times y, is divide Simplify as much as possible. (No decimals, leave as fractions)

8. Solve each equation for y 6y – 3x = -9 + 3x +3x 6y = 3x – 9 /6 /6 /6 y = 1x/2 - 3/2 Leave the y (in red), move everything else Opposite of -3x is +3x Can't combine 3x & -9 (not like terms) Opposite of 6 times y, is division Simplify as much as possible. Reduce fractions (No decimals, leave as fractions)

9. Solve each equation for y -5x – 8y = 15 +5x +5x – 8y = 5x + 15 /-8 /-8 /-8 y = -5x/8 - 15/8 Leave the y (in red), move everything else Opposite of -5x is +5x Can't combine 5x & 15 (not like terms) Opposite of -8 times y, is divide Negative / positive = negative (No decimals, leave as fractions)

10. Solve each equation for y 2x – y = 7 -2x -2x -y = -2x + 7 /-1 /-1 /-1 y = 2x - 7 Leave the y (in red), move everything else Opposite of 2x is -2x Can't combine -2x & 7 (not like terms) divide both sides by negative 1 to make y positive Negative / negative = positive (2x) Positive / negative = negative (-7)

11. Solve each equation for y -2x – 3y = -6 +2x +2x -3y = 2x – 6 /-3 /-3 /-3 y = -2x/3 + 2 Leave the y (in red), move everything else Opposite of -2x is 2x Can't combine 2x & 7 (not like terms) Opposite of -3 times y, is division positive / negative =negative negative / negative =positive (+2) Divide or reduce fractions, no decimals.