Question

7. How many solutions does this system of equations have? Explain howyou know. *y=-42 +32x + 8y = 10

Answer 1

Given:

`\begin{gathered} y=-4x+3------1 \\ 2x+8y=10-----2 \end{gathered}`

Substitute y = -4x + 3 into equation 2

This gives

`2x+8(-4x+3)=10`

Simplify and solve for x

`\begin{gathered} 2x-32x+24=10 \\ -30x=10-24 \\ -30x=-14 \\ x=(-14)/(-30) \\ x=(7)/(15) \end{gathered}`

Substitute x = 7/15 into equation 1

This gives

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

Solve for y

`\begin{gathered} y=-(28)/(15)+3 \\ y=(-28+45)/(15) \\ y=(17)/(15) \end{gathered}`

Therefore, there are two solution

`x=(7)/(15),y=(17)/(15)`