# How do you solve these for s and t using the following equations?: 3s-5t=-30 and 7s+11t=32

Oct 21, 2015

$s = - 2.5$ $t = 4.5$

#### Explanation:

You first need to find the equation in terms of either $s$ or $t$. I'm gonna do it in $s$.

So
=$3 s - 5 t = - 30$
=$3 s = - 30 + 5 t$
=$s = \frac{- 30 + 5 t}{3}$ ------ (1)

$7 s + 11 t = 32$
$7 s = 32 - 11 t$
$s = \frac{32 - 11 t}{7}$ ------ (2)

Now equate the 2 terms of $s$

= $\frac{- 30 + 5 t}{3} = \frac{32 - 11 t}{7}$

=$7 \left(- 30 + 5 t\right) = 3 \left(32 - 11 t\right)$

=$- 210 + 35 t = 96 - 33 t$

=$- 210 - 96 = - 35 t - 33 t$

=$- 306 = - 68 t$

=$t = \frac{- 306}{-} 68$

=$t = 4.5$

Now swap the value of t in an original equation,

$s = \frac{- 30 + 5 \left(4.5\right)}{3}$

$s = - \frac{7.5}{3}$

Therefore,

$s = - 2.5$ $t = 4.5$