5 .2 Solving Systems Using Substitution

1. 5.2 Solving Systems Using Substitution I can solve systems of linear equations by using substitution.

2. Solve one of the equations for one of the variables. • Isolate one of the variables in one of the equations. • Choose whichever seems easiest. • Substitute the expression for the variable in the other equation. • Use substitution when a system has at least one equation that can be solved quickly for one of the variables. How to Use Substitution

3. Solve the following system: • 3y + 4x = 14 • -2x + y = -3 • The second equation looks easiest to solve for y • So y = 2x – 3 • Substitute 2x – 3 for y in the other equation • 3(2x – 3) + 4x = 14 • Solve for x • x = 2.3 • Now substitute 2.3 for x in either equation • y = 1.6 • The solution is (2.3, 1.6) Practice

4. Solve the following system by substituting: • y = 3x and x + y = -32 • (-8, -24) Try This

5. Solve the system using substitution • 6y + 5x = 10 • x + 3y = -7 • (8, -5) You Try

6. A large snack pack costs $5 and a small costs $3. If 60 snack packs are sold, for a total of $220, How many were large and how many were small? • Let x = large and y = small • Money: 5x + 3y = 220 • Amount sold: x + y = 60 • Solve: (20, 40) • 20 large and 40 small Using Systems