Question

-x+5y=8 3x+7y=-3 find the equation​

Answer 1

Answer:

The solution to the system of equations be:

$x=-\frac{71}{22},\:y=\frac{21}{22}$

Step-by-step explanation:

Given the system of equation

$\begin{bmatrix}-x+5y=8\\ 3x+7y=-3\end{bmatrix}$

Multiply -x+5y=8 by 3:   -3x+15y=24

$\begin{bmatrix}-3x+15y=24\\ 3x+7y=-3\end{bmatrix}$

Add the equations

$3x+7y=-3$

$+$

$\underline{-3x+15y=24}$

$22y=21$

solving 22y=21 for y

$22y=21$

Divide both sides by 22

$\frac{22y}{22}=\frac{21}{22}$

Simplify

$y=\frac{21}{22}$

For -3x+15y=24  plug in y = 21/22

$-3x+15\cdot \frac{21}{22}=24$

Subtract 15 · 21/22 from both sides

$-3x+15\cdot \frac{21}{22}-15\cdot \frac{21}{22}=24-15\cdot \frac{21}{22}$

$-3x=\frac{213}{22}$

Divide both sides by -3

$\frac{-3x}{-3}=\frac{\frac{213}{22}}{-3}$

$x=-\frac{71}{22}$

The solution to the system of equations be:

$x=-\frac{71}{22},\:y=\frac{21}{22}$