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

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Presentation transcript:

Warm Up Check to see if the point is a solution for the system of linear equations. 1) 3x + 2y = 4 2) x + y = -2 –x + 3y = 5 2x + 3y = -3 (2, -1) (-3, 1) Find the solution for each graphed system.

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.

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

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).

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)

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)

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)

Classwork/ Homework Worksheet 8.1 & 8.2-all