5.1 -Systems of Linear Equations

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Presentation transcript:

5.1 -Systems of Linear Equations System of linear equations contains two or more linear equations with the same variable. Example: x + y = 3 x – y = -4

Graphing Systems of Linear Equations Where two lines cross it’s called the point of intersection. This point is a solution to both equations. Slope-Intercept Form y = mx + b (m = slope, b = y-int) y = -x + 3 y = x + 1

Find the Solution to the system of Linear Equations.

Checking the solution (1 , 2) y = -x + 3 (2) = -(1) + 3 2 = -1 + 3 2 = 2 Yes is a solution. y = x + 1 (2) = (1) + 1 2 = 2 Yes is a solution.

Find the Solution of the System of Linear Equations. 3x + 2y = 4 3(2) + 2(-1) = 4 6 – 2 = 4 4 = 4 -x + 3y = -5 -(2) + 3 (-1) = -5 -2 – 3 = -5 -5 = -5

Check the point and see if it’s a solution to the system of linear equations. x + y = -2 2) x – y = 2 2x – 3y = -9 x + y = 4 (-2, 1) (3, 1) x + y = 4 4) x – y = 5 2x + y = 5 2x + 3y = 0 (1, 0) (3, -2)

Homework Page 152 #5-6, 45-47, 54 Page 255-256 #1-4, 10-20 All