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Day 3: Solving a System of Equations by Substitution Warm-Up Solve the following system graphically. How many solutions does this system have? Sometimes it is difficult to identify the exact solution to a system by graphing. In this case, you can use a method called substitution. The first goal when using substitution is to reduce the system to one equation that has only one variable. Observe the following example. Example #1 Solve the system by substitution. y = 3x y=x–2 12 Example #2 Solve by substitution. Exercise Solve each system of equations by substitution. NOTICE that substitution is EASIER when you are plugging in for the variable that has a coefficient of 1. Keep this in mind, OK? 13 Example #3 Solve –2x + y = 8 3x + 2y = 9 by substitution. Example #4 Solve the following system by substitution. 14 Homework: Day 3 Solve by substitution. y= x+3 y = 2x + 5 x + 2y = –1 x–y=5 x = 2y – 4 x + 8y = 16 x = 6y – 11 3x – 2y = –1 15 Solve each system by graphing. Then use substitution to confirm your answer algebraically. Substitution: Substitution: 16
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