1. 6-2 SOLVING LINEAR SYSTEMS BY SUBSTITUTION Goal: Use substitution to solve a linear system Eligible Content: A1.1.2.2.1 / A1.1.2.2.2

2. Vocabulary  Substitution Method – a method of solving a system of equations that involves plugging one equation into the other equation.

3. Steps 1. Get one variable alone (look for a variable that does not have a number connected to it) 2. Replace that variable in the other equation with the expression after the equal sign. Solve for the remaining variable. 3. Plug your answer into the answer from step 1 to solve for the other variable. 4. Write your answer as an ordered pair. 5. Check your answer!

4. -2x + 2y = 2 2x + y = -2 2x + y = -2 -2x y = -2x – 2 y = -2*-1 – 2 y = 0 Answer: (-1, 0) -2x + 2y = 2 -2x + 2(-2x – 2) = 2 -2x – 4x – 4 = 2 -6x – 4 = 2 +4 +4 - 6x = 6 -6 -6 x = -1

5. Examples 1. 2x + 2y = 3 x – 4y = -1 (1, 0.5) 2. 3x + y = 3 7x + 2y = 1 (-5, 18) 3. 2x – y = -1 2x + y = -1 (-0.5, 0) 4. 2x + y = 4 -3x + 3y = 3 (1, 2)

6. A.(–2, 6) B.(–3, 3) C.(2, 14) D.(–1, 8) Use substitution to solve the system of equations. –3x + y = 12 –4x + 2y = 20

7. Practice Solve each system by substitution. 1. x + y = 1 2x – y = 2 2. -x + 4y = 10 x – 3y = 11 3. x – y = 0 x + y = 2 (1, 0) (74, 21) (1, 1)

8. Homework Page 347 #8-13