Question

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

Answer 1

Explanation:

1 solution

Answer 2

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} (-30x)/(-30)=(-14)/(-30) \\ x=(7)/(15) \end{gathered}`

Substitute x in the first equation and solve for y

`y=-4((7)/(15))+3=-(28)/(15)+3=(17)/(15)`

Solutions:

`\begin{gathered} x=(7)/(15) \\ y=(17)/(15) \end{gathered}`

Answer: The system has one solution