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Solving Systems by Elimination
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  • 1. Solving Systems By Elimination
  • 2.
    • Both equations must be in standard form.
    • The goal is to eliminate one of the variables.
    • You can add or subtract the equations to eliminate .
  • 3.
    • Solve the system by elimination:
    • 5x – 6y = -32
    • 3x + 6y = 48
    • 8x = 16
    • x = 2
    Line these two equations up. Look to if any of the variables would cancel each other out if the two equations were added or subtracted.
  • 4.
    • Substitute the x back into one of the equations to find the other variable.
    • 5(2) – 6y = -32
    • y = 7
    • The point of intersection is (2, 7)
  • 5.
    • Check your work.
    • Does the point work in both equations?
  • 6.
    • How do we solve?
    • x + y = 6
    • x + 3y = 10
    • Subtract (or multiply 2 nd equation by -1)
    • And the solution is . . .
    • (4, 2)
  • 7.
    • How do we solve?
    • 5x + 6y = 54
    • 3x - 3y = 17
    • Multiply the 2 nd equation by 2
    • And the solution is . . .
    • (8, 7/3)
  • 8.
    • How do we solve?
    • -a + 2b = -1
    • a = 3b - 1
    • 1 st , get that 2 nd equation in standard form. a – 3b = -1
    • And the solution is . . .
    • (5, 2)
  • 9.
    • How do we solve?
    • 2k – 3c = 6
    • 6k – 9c = 9
    • Multiply 1 st row by -3.
    • And the solution is . . .
    • No solution
    • What do you notice that helps you understand this is no solution?
  • 10.
    • How do we solve?
    • x + 4y = 1
    • 3x + 12y = 3
    • Multiply the 1 st one by -3
    • And the solution is . . .
    • Infinite number of solutions
    • What do you notice that helps you understand this is infinite number of solutions?