Process for Solving Linear Equations for the y Variable When working with linear equations, we will often be given equations of the form y mx b (m and b being constants), where the y-variable is already isolated. This makes our process of graphing much easier. However, equations are sometimes given to us in the form Ax By C (A, B, and C being constants), and we would like to solve for y. This is not a difficult process as long as we remember the basic principals of solving equations. 1. If any fractions or decimals occur in the equation, multiply through by the LCD to clear denominators and decimals. 2. Using the addition principal, add or subtract the entire Ax-term to move it to the other side of the equation. 3. Using the multiplication principal, divide both sides of the equation by B in order to isolate y. Be certain that BOTH the C and the Ax terms get divided by B! Notice in step two we will be using addition or subtraction. In step three we will be using division. We are "undoing" the equation so the various parts of the equation "let go" of the y. We want to start with the weakest connections (add/subtract), and then move to the stronger connections (multiply/divide). Think of it as moving backwards through the order of operations. Order of Operations P E Simplify Solve MD AS EXAMPLE #1: Solve 3x 2 y 7 for y 3x 2 y 7 3x 3x 2 y 3x 7 2 2 3x 7 y 2 2 3 7 y x 2 2 Subtracting 3x from both sides Dividing both sides by -2 Be sure BOTH terms are divided! Final, simplified answer EXAMPLE #2. Solve 1 2 15 x y 315 5 3 2 1 15 x 15 y 45 3 5 10 x 3 y 45 10 x 10 x 3 y 10 x 45 3 3 10 x 45 y 3 3 10 y x 15 3 2 1 x y 3 for y 3 5 Multiply both sides by LCD (15) Distribute 15 thru: every term must get multiplied by the 15! Add 10x to both sides Divide both sides by 3 Be sure BOTH terms get divided Final, simplified answer. EXAMPLE #3. Solve 3x y 12 for y 3 x y 12 3x 3x y 3 x 12 1 1 3 x 12 y 1 1 y 3 x 12 Subtract 3x from both sides Divide by -1 to get y instead of -y Both terms get divided. WATCH YOUR SIGNS! Final, simplified answer.