Solving Systems of Equations by Substitution

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Presentation transcript:

Solving Systems of Equations by Substitution Teacher Twins©2014

Warm Up (8, -2) (3, 9) No solution (4, 6)

Solving Systems of Equations by Substitution

4x-y=-4 4x-2x=-4 2x=-4 x = -2 Example 1 Solve the system by substitution. y=2x 4x-y=-4 Substitute 2x for y in the second equation. 4x-y=-4 4x-2x=-4 2x replaces the y because y = 2x 2x=-4 x = -2 Combine like terms and solve

Use y = 2x to find the value of y . Solve y=-4 The solution is (-2,-4).

Example 2 x=2y -x + y=-2 Substitute 2y for x in the second equation. Solve the system by substitution. x=2y -x + y=-2 Substitute 2y for x in the second equation. Notice when I substitute I have the same variable so I can solve the equation. -(2y) + y = -2 -y = -2 y = 2 Combine like terms and solve

Use x = 2y to find the value of x . The solution is (4, 2).

Ex 3: Solve the system by substitution. -3x + 3y = 4 -x + y = 3 y = x + 3 -3x + 3( x + 3) = 4 -3x + 3x + 9 = 4 9 = 4 is not true. The solution is no solution.

Ex 4: Solve the system by substitution. -3x + 3y = 12 -x + y = 4 y = x + 4 -3x + 3( x + 4) = 12 -3x + 3x + 12 = 12 12 = 12 is true. The solution is infinitely many solutions.

Practice Solve each system by substitution. 2x – 3y = -1 y = x – 1 2. 6x + 6y = - 6 5x + y = -13 The solution is (4, 3). The solution is (-3, 2).

Closure Explain why this method for solving systems of equations is called substitution.