ANSWER
The solution is where the two graphs intersect, which is
[tex](-3,1).[/tex]
EXPLANATION
The given system of equations are
[tex]y = \frac{1}{3} x + 2[/tex]
and
[tex]y = - x - 2[/tex]
We need to graph the two equations.
Let us graph
[tex]y = \frac{1}{3} x + 2[/tex]
first.
We need at least two points.
You can choose any appropriate value for x and solve for y. Choosing zero makes our working easier. So let us plot the intercepts.
When
[tex]x = 0[/tex]
[tex]\Rightarrow \: y = \frac{1}{3} (0) + 2[/tex]
[tex] \Rightarrow y = 0 + 2[/tex]
[tex] \Rightarrow y = 2[/tex]
So this gives us the ordered pair,
[tex](0,2)[/tex]
When
[tex]y = 0[/tex]
we get,
[tex]0= \frac{1}{3} x + 2[/tex]
[tex]\Rightarrow \: - 2 = \frac{1}{3} x[/tex]
[tex]\Rightarrow \: - 2 \times 3= x[/tex]
[tex]\Rightarrow \: -6= x[/tex]
This also gives the ordered pair
[tex](-6,0).[/tex]
We plot these two points and draw a straight line through them to obtain the blue graph in the attachment.
For the second line
[tex]
y = - x - 2[/tex]
We again find the intercepts and plot them.
When
[tex]x = 0[/tex]
[tex]y = - 0 - 2[/tex]
[tex]\Rightarrow \: y = - 2[/tex]
This gives the ordered pair
[tex](0,-2)[/tex]
Also, when
[tex]y = 0[/tex]
then we have,
[tex]0 = - x - 2[/tex]
[tex] 2 = - x[/tex]
[tex]x = - 2[/tex]
Then we again have the ordered pair,
[tex](-2,0)[/tex]
We plot these two points on the same graph sheet to obtain the red graph above.
The intersection of the two lines is
[tex](-3,1)[/tex]
You will get good grades so don't worry much.
