SOLUTION: for problems 7-9 solve the system of equations using addition to eliminate one variable. if the system has no solution, indicate that it is inconsistent. if it has infinite solutio

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Question 240710: for problems 7-9 solve the system of equations using addition to eliminate one variable. if the system has no solution, indicate that it is inconsistent. if it has infinite solutions, indicate that it is inconsistent. if it has infinite that it is dependent. if the system has a solution check your answer.
4x-3y=17
5x+y=7
check (if possible)
Answer by Stitch(187) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
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Equation 1: 4X+-+3Y+=+17
Equation 2: 5X+%2B+Y+=+7
Solution:
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Start by rewritting equation 2. Since Y is by itself, solve for Y
Equation 2: 5X+%2B+Y+=+7 Subtract 5X from both sides
Y+=+7+-+5X
Now you can plug (7-5X) into equation 1 for Y
Equation 1: 4X+-+3Y+=+17
4X+-+3%2A%287-5X%29+=+17 Simplify
4X+-+21+%2B+15X+=+17 Simplify
19X+-+21+=+17 Add 21 to both sides
19X+=+38 Divide both sides by 19
highlight%28X+=+2%29
To find Y, plug 2 in for X into the rewritten equation 2
Y+=+7+-+5X
Y+=+7+-+5%2A%282%29 Simplify
Y+=+7+-+10 Combine like terms
highlight%28Y+=+-3%29
Chesk Solution:
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Using X = 2 and Y = -3, solve equation 1
Equation 1: 4X+-+3Y+=+17
4%2A%282%29+-+3%2A%28-3%29+=+17
8+%2B+9+=+17
17+=+17