Question

Section 5.2-7. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).3x-y = 6-2x+2y = 8

Answer 1

We will solve the problem using the substitution method.

The system of equations to be solved is

`\begin{cases}3x-y=6 \\ -2x+2y=8\end{cases}`

Notice that the second equation is equivalent to

`\begin{gathered} -2x+2y=8 \\ \Leftrightarrow(1)/(2)(-2x+2y)=(1)/(2)(8) \\ \Leftrightarrow-x+y=4 \end{gathered}`

Then,

`\Rightarrow y=4+x`

We can substitute the last result into the first equation of the system as shown below

`\begin{gathered} 3x-y=6 \\ \Rightarrow3x-(4+x)=6 \\ \Rightarrow3x-4-x=6 \\ \Rightarrow2x=6+4=10 \\ \Rightarrow x=5 \end{gathered}`

Finally,

`\begin{gathered} \Rightarrow y=4+(5)=9 \\ \Rightarrow y=9 \end{gathered}`

The answer is (x,y)=(5,9)