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Warm Up Check to see if the point is a solution for the

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1 Warm Up Check to see if the point is a solution for the
system of linear equations. 1) 3x + 2y = ) x + y = -2 –x + 3y = x + 3y = -3 (2, -1) (-3, 1) Find the solution for each graphed system.

2 5.2 Solving Linear Systems by Substitution
EQ: How can you use substitution to solve a systems of linear equations? Rules for Solving Systems by Substitution: 1. Solve one of the equations for x or y. 2. In the other equation, substitute for the variable you solved for and solve. 3. Substitute the number back into one of the equations to solve for the other variable.

3 In the 1st equation, one variable is already solved (by itself).
Example 1: y = 4x x + y = 5 Solve by substitution In the 1st equation, one variable is already solved (by itself). x = 5 So, substitute the 1st equation in to the 2nd where the y is. 4x 5x = 5 Solve for x. Now, substitute this back in to the original 2nd equation and solve for y. x = 1

4 y = 4 x x + y = 5 x = 1 (1) Substitute the x value in to the other equation and solve for y. y = 4 y = 4 The solution is (1, 4).

5 Solve by Substitution 3. y = x - 1 x + y = 3 4. 3x + 2y = -12 y = x - 1 2. x = -4 3x + 2y = 20 2. (-4, 16) 3. (2, 1) 4. (-2, -3)

6 Solve by Substitution 5. x = 1/2 y - 3 4x - y = 10 6. x = -5y + 4 3x + 15y = -1 7. 2x - 5y = 29 x = -4y + 8 5. (8, 22) 6. No solution 7. (12, -1)

7 Solve by Substitution 8. x =5y + 10 2x - 10y = 20 9. 4x + y = 0 x + 2y = -7 10. 2x - 3y = -24 x + 6y = 18 8. Many solutions 9. (1, -4) 10. (-6, 4)

8 Classwork/ Homework Worksheet 8.1 & 8.2-all


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