Question

How do you solve the system `y = 3x - 4` and `2x - y = 1` by graphing?

Answer 1

Solution: `x=3` and `y=5`

Explanation:

Step one. Solve both equations for `y`. The first equation you provided is already equal to `y`, so just copy it.

Then solve the second equation for `y`:

`2x-y=1`
`color(white)(..)+ycolor(white)(.)+y` `color(white)(..x)`add y to both sides
`2x=1+y`
`-1color(white)(.)-1` `color(white)(xxxx;)`subtract 1 from both sides
`2x-1=y`

Now, either plotting points or plugging into your graphing utility, you can first graph the first equation:

`graph{3x-4 [-1, 3, -6, 10]}`

Then, on the same graph paper, either plot points or plugging into your graphing utility, you draw the second graph on top of this one.

`graph{(y-2x+1)(y-3x+4)=0 [-0.4,4.5,-2,8]}`

Observing closely where they cross, gives the solution

`x=3` and `y=5`.