Question

10. How many solutions does this system of equations have? Explain how you know.y = -4x + 32x + 8y = 10

Answer 1

Solve the system

$\begin{gathered} y=-4x+3 \\ 2x+8y=10 \end{gathered}$

Substitute y in the second equation

$2x+8(-4x+3)=10$$\begin{gathered} 2x-32x+24=10 \\ -30x+24=10 \\ -30x+24-24=10-24 \\ -30x=-14 \end{gathered}$

Solve for x

$\begin{gathered} \frac{-30x}{-30}=\frac{-14}{-30} \\ x=\frac{7}{15} \end{gathered}$

Substitute x in the first equation and solve for y

$y=-4(\frac{7}{15})+3=-\frac{28}{15}+3=\frac{17}{15}$

Solutions:

$\begin{gathered} x=\frac{7}{15} \\ y=\frac{17}{15} \end{gathered}$

Answer: The system has one solution