Question

What is the solution to the system of linear equations?

Answer 1

(0,2)

Explanation:

The equations must be derived from the graph:

First, find the slope of f(x):

`m=(y_2-y_1)/(x_2-x_1)` let
`(x_1,y_1)=(-3,3)` and
`(x_2,y_2)=(3,1)`

`m=((1)-(3))/((3)-(-3))\\m=(-2)/(6)\\m=-(1)/(3)`

Then use
`y-y_1=m(x-x_1)`

`y-3=-(1)/(3)[x-(-3)]\\y-3=-(1)/(3)x-1\\y=-(1)/(3)x+2\\f(x)=-(1)/(3)x+2`

For g(x), let:

`(x_1,y_1)=(-3,0)\\(x_2,y_2)=(0,2)`

`m=((2)-(0))/((0)-(-3))\\m=(2)/(3)`

`y-0=(2)/(3)[x-(-3)]\\y=(2)/(3)x+2\\g(x)=(2)/(3)x+2`

Now, to solve for x, allow the two expressions written in terms of x equal each other.

`-(1)/(3)x+2=(2)/(3)x+2\\(-(1)/(3)x+2)+(1)/(3)x=((2)/(3)x+2)+(1)/(3)x\\2=x+2\\(2)-2=(x+2)-2\\x=0`

To solve for y, substitute 0 for x in f(x):

`y=-(1)/(3)x+2\\y=-(1)/(3)(0)+2\\y=0+2\\y=2`

So, the solution to this system of equations would be the ordered pair (0,2). This solution is seen on the graph as the intersection of the two lines.