# Solve the linear system of equations

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### Question Description

shyamnair3
School: Duke University

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$\\ \frac{7}{4}x-\frac{5}{2}y=2---(1)\\ \\ \frac{1}{4}x+\frac{7}{2}y=8---(2)$

Multiply equation (1) and (2) by 4 to remove the fractions.

$\\ 4\times\frac{7}{4}x-4\times\frac{5}{2}y=4\times2\\ \\ 7x-10y=8---(3)\\ \\ 4\times\frac{1}{4}x+4\times\frac{7}{2}y=4\times8\\ \\ x+14y=32---(4)$

Multiply equation (4) by 7

7x + 98y = 224 ---(5)

Subtract equation (3) from equation (5)

7x + 98y - (7x - 10y) = 224 - 8

7x + 98y - 7x + 10y = 216

108y = 216

y = 216/108

y = 2

Substitute value of y in equation (4)

x + 14(2) = 32

x + 28 = 32

x = 32 - 28

x = 4

So solution is (4, 2).

x = 4, y = 2

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