Lesson 0 – 8 Systems of Linear Equations

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Lesson 0 – 8 Systems of Linear Equations Geometry Lesson 0 – 8 Systems of Linear Equations Objective: Use graphing, substitution, and elimination to solve systems of equations.

one solution (2, 1) y = -x + 3 y = 2x - 3 Solve by graphing, then state whether one solution, no solution, or infinitely many. y = -x + 3 y = 2x - 3 one solution (2, 1)

Solve by graphing… y – 2x = 6 3y – 6x = 9 y = 2x + 6 y = 2x + 3 Easier to graph if you use slope-intercept form. y – 2x = 6 3y – 6x = 9 y = 2x + 6 y = 2x + 3 No solution

The equations are the same which means they Solve by graphing y = 3x + 1 2y = 6x + 2 Solve for y y = 3x + 1 The equations are the same which means they have the same graph. Infinitely many solutions

Solve by substitution y = 5 3x = 5 y = 3x -2y + 9x = 5 -2(3x) + 9x = 5 Plug x back in to find y. y = 3x -2y + 9x = 5 -2(3x) + 9x = 5 y = 5 -6x + 9x = 5 3x = 5

Solve by substitution 2(-4x) + 3x = 8 -8x + 3x = 8 y = -4x 2y + 3x = 8 Plug x back in to find y. y = -4x 2y + 3x = 8 2(-4x) + 3x = 8 -8x + 3x = 8 -5x = 8

Plug into either equation Solve by Elimination Plug into either equation to find y. 3x + 2y = 7 4x + 2y = 0 4(-7) + 2y = 0 -x = 7 2y = 28 x = -7 y = 14 (-7, 14)

(-1, 2) Solve by Elimination 3x + 5y = 7 4x + 2y = 0 12x + 20y = 28 Pick which variable to eliminate. (4) 3x + 5y = 7 4x + 2y = 0 (3) 12x + 20y = 28 12x + 6y = 0 Plug in to find other variable. 4x + 2(2) = 0 4x + 4 = 0 14y = 28 4x = -4 y = 2 x = -1 (-1, 2)

Homework Pg. P18 1 – 15 all