Question

Find the point where the lines f(x)=3x−1 and g(x)=−2x+3 intersect. Show your work.

Answer 1

Given the equations of the lines as follows:

`\begin{gathered} f\mleft(x\mright)=3x-1 \\ g\mleft(x\mright)=-2x+3 \end{gathered}`

We will find the point of intersection between the lines

The condition of the intersection is f(x) = g(x)

so, we can write the following equation:

`3x-1=-2x+3`

Solve the equation to find x, combine the like terms:

`\begin{gathered} 3x+2x=3+1 \\ 5x=4 \\ x=(4)/(5)=0.8 \end{gathered}`

Substitute with x into the first equation to find the coordinates of y:

`y=3\cdot0.8-1=2.4-1=1.4`

So, the answer will be the point of intersection will be:

`(x,y)=(0.8,1.4)`