Question

X+y=18x=4+ysolve using systems of equations

Answer 1

Use the substitution method to solve the system of equations:

`\begin{gathered} x+y=18 \\ x=4+y \end{gathered}`

Since x is already isolated on the second equation, replace x with the expression for x in the first equation:

`\begin{gathered} x+y=18 \\ \Rightarrow(4+y)+y=18 \\ \Rightarrow4+2y=18 \\ \Rightarrow2y=18-4 \\ \Rightarrow2y=14 \\ \Rightarrow y=(14)/(2) \\ \therefore y=7 \end{gathered}`

Substitute y=7 into the expression for x:

`\begin{gathered} x=4+y \\ \Rightarrow x=4+7 \\ \therefore x=11 \end{gathered}`

Therefore, the solution for this system of equations, is:

`\begin{gathered} x=11 \\ y=7 \end{gathered}`