5.2 Solving Systems Using Substitution

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Presentation transcript:

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

How to Use Substitution 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

Practice 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

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

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

A large snack pack costs $5 and a small costs $3 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