Lesson Objective: I will be able to … Solve systems of linear equations in two variables by substitution Language Objective: I will be able to … Read, write, and listen about vocabulary, key concepts, and examples

Solving Systems of Equations by Substitution Page 5 Solving Systems of Equations by Substitution Step 2 Step 3 Step 4 Step 5 Solve for one variable in at least one equation, if necessary. Step 1 Substitute the resulting expression into the other equation. Solve that equation to get the value of the first variable. Substitute that value into one of the original equations and solve. Write the values from steps 3 and 4 as an ordered pair, (x, y), and check.

  Example 1: Solving a System of Linear Equations by Substitution Page 6 Solve the system by substitution. y = 3x Step 4 y = 3x y = x – 2 y = 3(–1) y = –3 Step 1 y = 3x Step 5 (–1, –3) y = x – 2 Step 2 y = x – 2 3x = x – 2 Check Substitute (–1, –3) into both equations in the system. Step 3 –x –x 2x = –2 y = 3x –3 3(–1) –3 –3  y = x – 2 –3 –1 – 2 –3 –3  2 2 x = –1

  Example 2: Solving a System of Linear Equations by Substitution Page 7 Solve the system by substitution. Step 4 y = x + 1 y = x + 1 y = 1 + 1 4x + y = 6 y = 2 Step 1 y = x + 1 Step 5 (1, 2) Step 2 4x + y = 6 4x + (x + 1) = 6 Check Substitute (1, 2) into both equations in the system. 5x + 1 = 6 Step 3 –1 –1 5x = 5 y = x + 1 2 1 + 1 2 2  4x + y = 6 4(1) + 2 6 6 6  5 5 x = 1

  Your Turn 2 Solve the system by substitution. x = 2y – 4 Step 4 Page 8 Solve the system by substitution. x = 2y – 4 Step 4 x + 8y = 16 x + 8y = 16 x + 8(2) = 16 Step 1 x = 2y – 4 x + 16 = 16 (2y – 4) + 8y = 16 x + 8y = 16 Step 2 x = 0 – 16 –16 Step 5 (0, 2) Step 3 10y – 4 = 16 +4 +4 10y = 20 Check Substitute (0, 2) into both equations in the system. 10 10 x = 2y – 4 0 2(2) – 4 0 0  x + 8y = 16 0 + 8(2) 16 16 16  y = 2

Example 3: Using the Distributive Property Page 9 y + 6x = 11 Solve by substitution. 3x + 2y = –5 Step 1 y + 6x = 11 Step 3 – 6x – 6x 3x + 2(–6x) + 2(11) = –5 3x – 12x + 22 = –5 y = –6x + 11 3x + 2(–6x + 11) = –5 3x + 2y = –5 Step 2 –9x + 22 = –5 –9x = –27 – 22 –22 –9 –9 Step 4 y + 6x = 11 x = 3 y + 6(3) = 11 Step 5 (3, –7) y + 18 = 11 –18 –18 y = –7

When you solve one equation for a variable, you must substitute the value or expression into the other original equation, not the one that had just been solved. Caution

Your Turn 3 –2x + y = 8 Solve by substitution. 3x + 2y = 9 Page 10 –2x + y = 8 Solve by substitution. 3x + 2y = 9 Step 1 –2x + y = 8 Step 3 + 2x +2x y = 2x + 8 3x + 2(2x) + 2(8) = 9 3x + 4x + 16 = 9 3x + 2(2x + 8) = 9 3x + 2y = 9 Step 2 7x + 16 = 9 7x = –7 –16 –16 Step 4 –2x + y = 8 7 7 –2(–1) + y = 8 x = –1 y + 2 = 8 Step 5 (–1, 6) –2 –2 y = 6

Classwork Assignment #31 6-2 Practice B / 6-1 Practice C Worksheet

Homework Assignment #31 Finish 6-2 / 6-1 Worksheet Holt 6-2 #8 – 11, 15, 17, 24, 25, 36, 37 KIN 6-3