1. Systems of Equations By Dr. Marinas

2. Solving Systems Graphing Method Substitution Method Elimination (or Adding) Method

3. Graphing Method Graph each equation carefully Find the point of Intersection Check solution in BOTH equations x + 4 y = 3 (Eq. 1) 3x - 2y = -5 (Eq. 2) Eq. 1 goes through (3, 0) and (0, 3/4) Eq. 2 goes through (0, 5/2) and (-5/3, 0)

4. Substitution Method Solve one of the Equations for one of the variables Substitute this value into the other equation Solve for the variable Substitute this value into either equation to find the other value x + 4 y = 3 (Eq. 1) 3x - 2y = -5 (Eq. 2) Take Eq. 1 and solve for x: x = 3 - 4y Substitute 3 - 4y into Eq. 2 for x 3(3 - 4y) - 2y = -5 Solve for y. 9 - 12y - 2y = -5 9 - 14y = -5 and -14y = -14 y = 1 Replace y with 1 in Eq. 1 and solve for x. x + 4 = 3 (-1, 1)

5. Elimination (Adding) Method Look at the system and decide what variable you are going to eliminate Multiply (If necessary) so that when added a variable is eliminated. Solve for that variable and then substitute into either equation x + 4 y = 3 (Eq. 1) 3x - 2y = -5 (Eq. 2) Multiply Eq. 2 by 2 and add to Eq. 1 to eliminate the y’s. x + 4 y = 3 (Eq. 1) 6x - 4y = -10 2(Eq. 2) ---------------- 7x = - 7 so x = -1 By substitution y = 1 (-1, 1)