How do you solve 3x+4y=22 and x-5y=-37?

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Answer 1 · 2015-09-09T06:08:32

The solution for the system of equations is
$x = - 2, y = 7$ $color(blue)(x=-2, y=7$

$3 x + 4 y = 22$ $color(blue)(3x)+4y=22$ ...........equation $(1)$ $(1)$

$x - 5 y = - 37$ $x-5y=-37$ , multiplying this equation by $3$ $3$
$3 x - 15 y = - 111$ $color(blue)(3x)-15y=-111$ ....equation $(2)$ $(2)$

Now we can solve using the method of elimination .

Subtracting equation $2$ $2$ from $1$ $1$ eliminates $3 x$ $color(blue)(3x$

$3 x + 4 y = 22$ $color(blue)(3x)+4y=22$
$-cancelcolor(blue)(3x)+15y=+111$

$19y = 133$
$color(blue)(y=7$

Now we find $x$ by substituting $y$ in equation $1$
$3x+4y=22$

$3x=22 -4y$

$3x=22 -4*7$

$3x=22 -28$

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