Question #02b23

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Answer 1 · 2017-03-29T10:46:26

$(x, y) = (- \frac{4}{3}, \frac{2}{3})$ $(x,y)=(-4/3,2/3)$

I've no idea what the leading $(- 3, 1)$ $(-3,1)$ means.

Since this was asked under the heading "Systems Using Substitution", I will demonstrate how to solve the given two equations (using substitution.

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

Rewriting [1] as a definition in terms of $x$ $x$
[3] $XXX x = y - 2$ $color(white)("XXX")x=y-2$

We can now substitute $y - 2$ $y-2$ for $x$ $x$ in equation [2]
[4] $XXX (y - 2) + 5 y = 2$ $color(white)("XXX")(y-2) +5y=2$

$\to$ $rarr$ [5] $XXX 6 y = 4$ $color(white)("XXX")6y=4$

$\to$ $rarr$ [6] $XXX y = \frac{2}{3}$ $color(white)("XXX")y=2/3$

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

$\to$ $rarr$ [8] $XXX x = - \frac{6}{3} + \frac{2}{3} = - \frac{4}{3}$ $color(white)("XXX")x=-6/3+2/3=-4/3$