How do you solve 3y = 14 + x and x + 22 = 5y?

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Answer 1 · 2015-09-09T06:12:54

The solution for the system of equations is
$color(blue)(x=-2, y=4$

$3y = 14 + x$ ....equation $(1)$

$x + 22 = 5y$
$x=color(blue)( 5y-22$ ......equation $(2)$

We can solve using the method of substitution.
Substituting equation $2$ in equation $1$ :

$3y = 14 + x$

$3y = 14 +color(blue)( 5y-22$

$3y = -8+ 5y$
$8 = 5y- 3y$

$2y=8$
$color(blue)(y=4$

Now we find $x$ by substituting $y$ in equation 2:
$x= 5y-22$

$x= 5*4-22$

$x= 20-22$

$color(blue)(x=-2$