-x+5y=8 3x+7y=-3 find the equation​

Sagot :

Answer:

The solution to the system of equations be:

[tex]x=-\frac{71}{22},\:y=\frac{21}{22}[/tex]

Step-by-step explanation:

Given the system of equation

[tex]\begin{bmatrix}-x+5y=8\\ 3x+7y=-3\end{bmatrix}[/tex]

Multiply -x+5y=8 by 3:   -3x+15y=24

[tex]\begin{bmatrix}-3x+15y=24\\ 3x+7y=-3\end{bmatrix}[/tex]

Add the equations

[tex]3x+7y=-3[/tex]

[tex]+[/tex]

[tex]\underline{-3x+15y=24}[/tex]

[tex]22y=21[/tex]

solving 22y=21 for y

[tex]22y=21[/tex]

Divide both sides by 22

[tex]\frac{22y}{22}=\frac{21}{22}[/tex]

Simplify

[tex]y=\frac{21}{22}[/tex]

For -3x+15y=24  plug in y = 21/22

[tex]-3x+15\cdot \frac{21}{22}=24[/tex]

Subtract 15 · 21/22 from both sides

[tex]-3x+15\cdot \frac{21}{22}-15\cdot \frac{21}{22}=24-15\cdot \frac{21}{22}[/tex]

[tex]-3x=\frac{213}{22}[/tex]

Divide both sides by -3

[tex]\frac{-3x}{-3}=\frac{\frac{213}{22}}{-3}[/tex]

[tex]x=-\frac{71}{22}[/tex]

The solution to the system of equations be:

[tex]x=-\frac{71}{22},\:y=\frac{21}{22}[/tex]