Question

8 - 53: solve each system of equations below. (leave answers as fractions if needed)
a. 2x + y=-7y 2x=-8(x + 10) y = x + 10
b. 3x=-5y 6x - 7y = 17

Explanation:

Step1: Solve part a

First, simplify the first - equation $2x + y=-7y$ to $2x=-8y$. Then substitute $y = x + 10$ into $2x=-8y$. We get $2x=-8(x + 10)$.
$2x=-8x-80$.
Add $8x$ to both sides:
$2x + 8x=-80$.
$10x=-80$.
$x=-8$.
Substitute $x = - 8$ into $y=x + 10$, then $y=-8 + 10=2$.

Step2: Solve part b

From $3x=-5y$, we can express $x=-\frac{5}{3}y$.
Substitute $x = -\frac{5}{3}y$ into $6x-7y = 17$.
$6\times(-\frac{5}{3}y)-7y = 17$.
$-10y-7y = 17$.
$-17y = 17$.
$y=-1$.
Substitute $y=-1$ into $x = -\frac{5}{3}y$, then $x=\frac{5}{3}$.

Answer:

a. $x=-8,y = 2$
b. $x=\frac{5}{3},y=-1$