Solving Systems of Equations

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Presentation transcript:

Solving Systems of Equations Substitution Method Liberty Hill Middle School Mrs. Book Algebra I 11/14/2018

Substitution Method You can create a one-variable equation by replacing one variable with an equivalent expression containing the other variable. 11/14/2018

Steps for Using the Substitution Method Step 1: Solve one of the equations for one of the variables Step 2: Substitute the expression from Step 1 into the other equation and solve for the other variable Step 3: Substitution the value from Step 2 into one of the original equations and solve. 11/14/2018

Solve the system of linear equations by substitution y = -2x – 9 6x – 5y = -19 Equation 1 is already solved for y Substitute -2x – 9 for y in Equations 2 and solve for x 6x – 5(-2x – 9) = - 19 6x + 10x + 45 = -19 16x = -45 – 19 16x = -64 x = -4 11/14/2018

Solve the system of linear equations by substitution y = -2x – 9 6x – 5y = -19 x = -4 Substitute -4 in for x in Equation 1 and solve for y y = -2(-4) – 9 y = 8 – 9 y = -1 The solution is (-4, -1) 11/14/2018

* 07/16/96 Solve the system of linear equations by substitution. Check your solution. y = 3x + 14 y = -4x (-2, 8) 11/14/2018 *

* 07/16/96 Solve the system of linear equations by substitution. Check your solution. 3x + 2y = 0 y = ½x - 1 (½, -¾) 11/14/2018 *

* 07/16/96 Solve the system of linear equations by substitution. Check your solution. -x + y = 3 3x + y = - 1 (-1, 2) 11/14/2018 *

* 07/16/96 Solve the system of linear equations by substitution. Check your solution. x - 2y = 7 3x - 2y = 3 (-2, -9/2) 11/14/2018 *

Summary Solve one equation for one of the variables Substitution the expression from Step 1 into the other equation and solve for the other variable Substitute the value from Step 2 into one of the original equation and solve. 11/14/2018