Question

Write the equation of the line that it is parallel to y = 2x + 1 and passes through the solution of the following system equations

Answer 1

First, let's solve the system:

`\begin{cases}3x-2y=10 \\ x+y=5\end{cases}`

Clearing y from equation 2, substituting in equation 1 and solving for x :

`\begin{gathered} x+y=5\rightarrow y=5-x \\ 3x-2y=10 \\ \rightarrow3x-2(5-x)=10 \\ \rightarrow3x-10+2x=10 \\ \rightarrow5x=20 \\ \Rightarrow x=4 \end{gathered}`

Substituting and solving for y :

`\begin{gathered} y=5-x \\ \Rightarrow y=1 \end{gathered}`

We get that the solution for the system is:

`(4,1)`

In order for two lines to be parallel, they need to have the same slope. This means that we'll use a slope of 2.

Using this, the point calculated and the slope-point form:

`\begin{gathered} y-1=2(x-4) \\ \rightarrow y-1=2x-8 \\ \rightarrow y=2x-7 \end{gathered}`

We get that the equation of the line that is parallel to y = 2x+1 and passes through (4 ,1) is:

`y=2x-7`