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How do you solve the following linear system: $- 2 x + 5 y = 4, 4 x + 5 y = - 2$ $-2x+5y=4, 4x+5y=-2$ ?

1 Answer

Alan P. · Stefan V.

Feb 8, 2016

$(x, y) = (- 1, \frac{2}{5})$ $(x,y)=(-1,2/5)$

Explanation:

Given
[1] $XXX - 2 x + 5 y = 4$ $color(white)("XXX")-2x+5y=4$
[2] $XXX 4 x + 5 y = - 2$ $color(white)("XXX")4x+5y=-2$

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

Divide both sides of [3] by $6$ $6$
[4] $XXX x = - 1$ $color(white)("XXX"color(green)(x=-1)$

Substitute $(- 1)$ $(-1)$ from [4] for $x$ $x$ in [1]
[5] $XXX - 2 \times (- 1) + 5 y = 4$ $color(white)("XXX")-2xx(-1)+5y=4$

Simplify [5]
[6] $XXX 5 y = 2$ $color(white)("XXX")5y=2$

Divide both sides of [6] by $5$ $5$
[7] $XXX y = \frac{2}{5}$ $color(white)("XXX")color(green)(y=2/5)$

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