Question

use the method of substitution to solve the following system of equations. if the system is dependent, express the solution set in terms of one of the variables. leave all fractional answers in fraction form.

Answer 1

`\begin{gathered} \text{Given} \\ -3x+y=11 \\ -2x=-36 \end{gathered}`

Solve for x by using the second equation

`\begin{gathered} -2x=-36 \\ \text{Divide both sides by }-2 \\ (-2x)/(-2)=(-36)/(-2) \\ \frac{\cancel{-2}x}{\cancel{-2}}=(-36)/(-2) \\ x=18 \end{gathered}`

Now that we have solve for x, substitute the value of x to the first equation

`\begin{gathered} -3x+y=11 \\ \text{Substitute }x=18 \\ -3(18)+y=11 \\ -54+y=11 \\ y=11+54 \\ y=65 \end{gathered}`

Therefore, the solution to the system of equations is x = 18, y = 65