Question

Solve the system by substitution × = 6y -22x +5y =47

Answer 1

We have the following system:

`\begin{gathered} x=6y-2\ldots(A) \\ 2x+5y=47\ldots(B) \end{gathered}`

Solving by substitution method.

If we substitute equation A into B, we get

`2(6y-2)+5y=47`

which gives

`12y-4+5y=47`

By combining similar terms, we have

`\begin{gathered} 12y+5y-4=47 \\ 17y-4=47 \end{gathered}`

If we move -4 to the right hand side, we obtain

`\begin{gathered} 17y=47+4 \\ 17y=51 \end{gathered}`

Then, if we move the coefficient of y to the right hand side, wehave

`\begin{gathered} y=(51)/(17) \\ y=3 \end{gathered}`

Then, we can substitute this result into equation A, which gives

`x=6(3)-2`

so, xi given by

`\begin{gathered} x=18-2 \\ x=16 \end{gathered}`

Therefore, the answer is

`\begin{gathered} x=16 \\ y=3 \end{gathered}`