How do you solve the system of equations: x - 2y = -1, 2x - y = 4?

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Answer 1 · 2015-08-14T11:46:46

The solutions are:
$color(blue)(x=3,y=2$

$x - 2y = -1$ , multiplying this equation by $2$
$color(blue)(2x) -4y = -2$ ....equation $(1)$

$color(blue)( 2x) - y = 4$ .........equation $(2)$

Now we can solve through elimination as we have the term $color(blue)(2x)$ common to both equations:

Subtracting equation $2$ from $1$

$cancel(color(blue)(2x)) -4y = -2$
$-cancel(color(blue)( 2x)) + y =- 4$

$-3y=-6$
$color(blue)(y=2$

Now we find $x$ by substituting $y$ in equation $1$
$x - 2y = -1$
$x = -1+2y$
$x=-1+2*(2)$
$x=-1+4$
$color(blue)(x=3$