Question #0dfc8

Dec 13, 2016

$\left(0 , 2\right)$

Explanation:

Normally I wouldn't make a grammatical comment, but it seems important here. The equations are lines that intersect; there is only one solution. The solution is the point where the two lines intersect.

Two equations, two variables. Use Gauss-Jordan Elimination
$- 4$ $- 1$ $- 2$
$8$ $- 2$ $- 4$

$\left(R o {w}_{1}\right) \cdot - 1 \implies R o {w}_{1}$
$4$ $1$ $2$
$8$ $2$ $- 4$

$\frac{R o {w}_{1}}{4} \implies R o {w}_{1}$
$1$ $\frac{1}{4}$ $\frac{1}{2}$
$8$ $- 2$ $- 4$

$\left(R o {w}_{1}\right) \cdot 8 - \left(R o {w}_{2}\right) \implies \left(R o {w}_{2}\right)$
$1$ $\frac{1}{4}$ $\frac{1}{2}$
$0$ $4$ $8$

$\frac{R o {w}_{2}}{4} \implies R o {w}_{2}$
$1$ $\frac{1}{4}$ $\frac{1}{2}$
$0$ $1$ $2$

$y = 2$
Substitute in to either equation to find that $x = 0$.

NOTE: This application could really use some matrix formatting.