SOLUTION: solve the system using any algebraic method x+2y=7 3x+5y=17

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Question 218708: solve the system using any algebraic method
x+2y=7
3x+5y=17
Found 2 solutions by drj, MathTherapy:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
solve the system using any algebraic method

x+2y=7
3x+5y=17

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+2%5Cy+=+7%2C%0D%0A++++3%5Cx+%2B+5%5Cy+=+7+%29%0D%0A++We'll use substitution. After moving 2*y to the right, we get:
1%2Ax+=+7+-+2%2Ay, or x+=+7%2F1+-+2%2Ay%2F1. Substitute that
into another equation:
3%2A%287%2F1+-+2%2Ay%2F1%29+%2B+5%5Cy+=+7 and simplify: So, we know that y=14. Since x+=+7%2F1+-+2%2Ay%2F1, x=-21.

Answer: system%28+x=-21%2C+y=14+%29.



I hope the above steps were helpful.

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And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
solve the system using any algebraic method
x+2y=7
3x+5y=17

x + 2y = 7 ------ (i)
3x + 5y = 17 -------(ii)
-3x - 6y = -21 -------(iii)--- Multiplying eq (i) by - 3
-y = - 4---- Adding eq (ii) and (iii)

y = %28-4%29%2F-1 = highlight_green%284%29

Substituting 4 for y in eq (i) to get: x + 2(4) = 7

x + 8 = 7

x = 7 - 8 = highlight_green%28-+1%29

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Check
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x + 2y = 7 ------- - 1 + 2(4) = 7 ----- - 1 + 8 = 7 (TRUE)
3x + 5y = 17 ------- 3(-1) + 5(4) = 17 ----- - 3 + 20 = 17 (TRUE)