Question

Solve y=5x-3 -x+7y=-21

Answer 1

Given the equation system:

`\begin{gathered} y=5x-3 \\ -x+7y=21 \end{gathered}`

You can find the solution to this equation system using the subtitution method.

Since the first expression is written in terms of y, you can replace it into the second expression and calculate for x

`\begin{gathered} -x+7y=21 \\ -x+7(5x-3)=21 \end{gathered}`

-Distribute the multiplication on the parentheses term:

`\begin{gathered} -x+7\cdot5x-7\cdot3=21 \\ -x+35x-21=21 \end{gathered}`

-Simplify the x-terms, by solving the operation between them

`34x-21=21`

-Pass 21 to the right side of the equation by applying the opposite operation to both sides of the equal sign

`\begin{gathered} 34x-21+21=21+21 \\ 34x=42 \end{gathered}`

-Finally, divide both sides of the equation by 34 to determine the value of x

`\begin{gathered} (34x)/(34)=(42)/(34) \\ x=(21)/(17) \end{gathered}`

Now that we have determined the value of x, we can replace it into the first equation to calculate the value of y:

`\begin{gathered} y=5x-3 \\ y=5((21)/(17))-3 \\ y=(105)/(17)-3 \\ y=(54)/(17) \end{gathered}`

This system has one solution at the point

`((21)/(17),(54)/(17))`