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7.4 Elimination using Multiplication. What you’ll learn: 1. To solve a system using multiplication. Elimination using multiplication. When opposites or the same coefficients for like-variables do not occur, you can create them by multiplying one or both equations by a number. Ex: 3x-4y=-5
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7.4 Elimination using Multiplication What you’ll learn: 1. To solve a system using multiplication
Elimination using multiplication When opposites or the same coefficients for like-variables do not occur, you can create them by multiplying one or both equations by a number. Ex: 3x-4y=-5 x+5y=9 If you multiply the 2nd equation by -3, opposites are created with the x-terms.
Focus on deciding what to multiply by: x-7y=9 7x-3y=2 Multiply 1stequ. by -7 2x-4y=8 -x-3y=2 Multiply 2ndequ. by 2 2x-5y=7 4x+2y=9 Multiply 1stequ. by -2 3x-6y=8 2x+5y=3 Multiply 1stequ. by 2 and 2ndequ. by -3 (but there are other options)
Examples • 2x+y=23 3x+2y=37 Mult. 1stequ. by -2 -4x-2y=-46 3x+2y=37 -x=-9 x=9 Plug into either original equ. to find y. 2(9)+y=23 18+y=23 y=5 Solution: (9,5) • 4x+3y=8 3x-5y=-23 Mult. 1stequ. by 5 and 2ndequ. by 3. 20x+15y=40 9x-15y=-69 29x=-29 x=-1 Find y: 4(-1)+3y=8 -4+3y=8 3y=12 y=4 Solution: (-1,4)
Try 2 • x+5y=4 3x-7y=-10 • 2x-4y=6 x-2y=3
