Question 620290: How would I solve this equation using multiplication with the addition method? Also by using elimination..not substitution.
5x - 2y = 4
3x + y = 9
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! Hi, there--
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Using multiplication with addition is the elimination method. Substitution is a different method.
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Elimination Method
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I notice that the first equation has a -2y and the second equation has a y. I'm going to MULTIPLY every term in the second equation by 2. Then I will ADD the two equations together to ELIMINATE the y-term.
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5x - 2y = 4 ==> 5x - 2y = 4
3x + y = 9 ===> 6x + 2y = 18
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Add the two equations together. Notice that -2y and 2y cancel each other out because their sum is 0. Since 5x+6x=11 and 4+18=22, we have
11x = 22
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Simplify.
x=2
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Now substitute 2 for x in either equation to find the y-value. I'll use the first.
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5x-2y=4
5(2)-2y=4
10-2y=4
-2y=-6
y=3
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Since x=2 and y=3, the ordered pair (2,3) in the solution to this system.
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Remember to check this ordered pair in the original equations to make sure you didn't make a error somewhere.
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5x - 2y = 4
5(2)-2(3) = 4
10-6 = 4
4 = 4 Check!
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3x + y = 9
3(2) +(3) = 9
6 + 3 = 9
9 = 9 Check!
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Hope this helps. Feel free to email if you still have questions about this.
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Ms. Figgy
math.in.the.vortex@gmail.com
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