Question

Solve each system by substitution.y =-2x + 5y =-8x+17

Answer 1

To solve the equation system by substitution, since the equations are expressed in terms of y, you have to equal both expressions and calculate the value of x:

`\begin{cases}y=-2x+5 \\ y=-8x+17\end{cases}`
`\begin{gathered} y=y \\ -2x+5=-8x+17 \end{gathered}`

To calculate the value of x, the first step is to pass the x-term to the left side of the equation by applying the opposite operation:

`\begin{gathered} -2x+8x+5=-8x+8x+17 \\ 6x+5=17 \end{gathered}`

Next, pass 5 to the right side of the equation:

`\begin{gathered} 6x+5-5=17-5 \\ 6x=12 \end{gathered}`

Finally, divide both sides by 6 to reach the value of x

`\begin{gathered} (6x)/(6)=(12)/(6) \\ x=2 \end{gathered}`

Now that we have determined the value of x, replace it in either one of the original equations to determine the value of y:

`\begin{gathered} y=-2x+5 \\ y=-2\cdot2+5 \\ y=-4+5 \\ y=1 \end{gathered}`

The solution for this equation system is (2,1)