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# Solving Systems by Elimination

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• what about multiplying 2 ND row by -2
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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.
• 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?