How do you solve the system of equations: x + 2y = 7, 2x + y = 8?

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Answer 1 · 2015-08-14T11:50:41

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

$x + 2y = 7$ , multiplying this equation by $2$
$color(blue)(2x )+ 4y = 14$ ,.......equation $1$

$color(blue)(2x) + y = 8$ ....equation $2$

Solving by elimination .

Subtracting equation $2$ from $1$ to eliminate $color(blue)(2x$

$cancel(color(blue)(2x ))+ 4y = 14$
$-cancel(color(blue)(2x)) - y =- 8$

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

Now, we find $x$ by substituting $y$ in equation $1$
$x + 2y = 7$

$x = 7-2y$

$x=7-2*2$
$x=7-4$
$color(blue)(x=3$