Question

Identify the solution to system graphed y=-3x +4 y = 3x - 2

Answer 1

`\mleft\{\begin{aligned}y=-3x+4 \\ y=3x-2\end{aligned}\mright.`

To find the solution for this system in a graph manner we need to graph both equations and look for the point at which they intercept.

For the first equation we know that the y-intercept is 4. So we will calculate the x-intercept by making y=0.

`\begin{gathered} 0=-3x+4 \\ 3x=4 \\ x=(4)/(3) \end{gathered}`

The first line goes through the points (0,4) and (4/3, 0).

For the second equation we know that the y-intercept is -2. So we will calculate the x-intercept by making y-.

`\begin{gathered} 0=3x-2 \\ 3x=2 \\ x=(2)/(3) \end{gathered}`

The second line goes through the points (0,-2) and (2/3,0).

To graph each line we can draw a line between the points that belong to it. We have:

Since the solution for the system is the point at which they cross, the ordered pair is (1,1).