Question

How do you solve the system by graphing `-3x+y=–3` and `y=x-3`?

Answer 1

See a solution process below:

Explanation:

We can first graph the line for the first equation. We can do this by solving for two points which solve the equation and plot these points and draw a straight line through the two points.:

First Point: For `x = 0`

`(-3 * 0) + y = -3`

`0 + y = -3`

`y = -3` or `(0, -3)`

Second Point: For `x = 1`

`(-3 * 1) + y = -3`

`-3 + y = -3`

`color(red)(3) - 3 + y = color(red)(3) - 3`

`0 + y = 0`

`y = 0` or `(1, 0)`

We can next plot the two points on the coordinate plane and draw the line:

graph{(-3x + y + 3)(x^2+(y+3)^2-0.025)((x-1)^2+y^2-0.025)=0 [-10, 10, -5, 5]}

We can follow this same process for the second equation.

First Point: For `x = 0`

`y = 0 - 3`

`y = -3` or `(0, -3)`

Second Point: For `x = 1`

`y = 1 - 3`

`y = -2` or `(1, -2)`

We can then plot the two points on the coordinate plane and draw the line:

graph{(y - x + 3)((x-1)^2+(y+2)^2-0.025)(-3x + y + 3)(x^2+(y+3)^2-0.05)((x-1)^2+y^2-0.025)=0 [-10, 10, -5, 5]}

We can see from the graph the two lines intersect at `(0, -3)`