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

1 Answer

Nov 17, 2015

$(x, y) = (\frac{4}{5}, - \frac{9}{5})$ $(x,y) = (4/5,-9/5)$

Explanation:

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

Subtract [2] from [1]
[3] $XXX - 5 y = 9$ $color(white)("XXX")-5y= 9$

Divide [3] by $(- 5)$ $(-5)$
[4] $XXX y = - \frac{9}{5}$ $color(white)("XXX")y= -9/5$

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

Substitute $(- \frac{9}{5})$ $(-9/5)$ from [4] for $y$ $y$ in [5]
[6] $XXX x - \frac{9}{5} = - 1$ $color(white)("XXX")x-9/5= -1$

Add $\frac{9}{5}$ $9/5$ to both sides of [6]
[7] $XXX x = \frac{4}{5}$ $color(white)("XXX")x=4/5$

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