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

User Dzikovskyy
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2 Answers

4 votes

Answer:

Explanation:

1 solution

User Donnell
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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

User Amin Shojaei
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