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How do you solve the following system: $2 x - y = 7, 2 x + 5 y = 5$ $2x-y=7, 2x +5y = 5$ ?

1 Answer

Dec 22, 2015

$(x, y) = (3 \frac{1}{3}, - \frac{1}{3})$ $(x,y)=(3 1/3, -1/3)$

Explanation:

Given:
[1] $XXX 2 x - y = 7$ $color(white)("XXX")2x-y=7$
[2] $XXX 2 x + 5 y = 5$ $color(white)("XXX")2x+5y=5$

Subtract [2] from[1]
[3] $XXX - 6 y = 2$ $color(white)("XXX")-6y=2$

Divide both sides by $(- 6)$ $(-6)$ (and reduce the resulting fraction)
[4] $XXX y = - \frac{1}{3}$ $color(white)("XXX")y=-1/3$

Substitute $(- \frac{1}{3})$ $(-1/3)$ for $y$ $y$ in [1]
[5] $XXX 2 x - (- \frac{1}{3}) = 7$ $color(white)("XXX")2x-(-1/3)=7$

Subtract $\frac{1}{3}$ $1/3$ from both sides
[6] $XXX 2 x = 6 \frac{2}{3}$ $color(white)("XXX")2x=6 2/3$

Divide both sides by $2$ $2$
[7] $XXX x = 3 \frac{1}{3}$ $color(white)("XXX")x=3 1/3$

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