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3.2 October 02, 2014 Get out your notes from yesterday. We will do the back side today. Bell Ringer Check your homework answers with your group Solve using substitution 3x+ 2y = 1 ­2x + y = 4 1. Solve one equation for a variable 2. Substitute the equation from 1. back into the other equation. 3. Solve 3.2 Solving Systems Algebraically Substitution: • Good to use when one equation is already solved for a variable • Useful if at least one variable has a coefficient of +1 or ­1. Elimination • Works well with any equation • Goal is to start by rewriting the equations so one variable has opposite coefficients. Solve using elimination 1. Pick a variable to eliminate. 8x + 2y = 4 ­2x + 3y = 13 2. Multiple one or both equations by a real number so that selected variable has opposite coefficients 3. Add equations and solve for remaining variable. 4. Substitute solution from step 3 back into any of the equations to find the remaining variable. 4. Substitute solution back into equation from step 1. Solve 12x ­ 3y = ­9 ­4x + y = 3 Solve 6x + 15y = ­12 ­2x ­ 5y = 9 3.2 October 02, 2014 HW 3.2 Worksheet G # 1­9, 11­19, 21­29