Answer: the solution of the sytem is x = 4, y = 11/3.
Explanation:
There are multiple ways to solve this, you could just graph the other line and see at which point both lines intersect, that point is the solution of the system.
I will do it in a more analytical way.
We have the two equations:
y = -(1/3)*x + 5
y = (5/3)*x - 3
x and y represent the same number.
then we must have y = y
then we can write:
-(1/3)*x + 5 = y = (5/3)*x - 3
this means that:
-(1/3)*x + 5 = (5/3)*x - 3
Now we can solve this for x.
To do it, let's move all the terms with x to the left, and the terms without x to the right:
-(1/3)*x - (5/3)*x = -3 - 5
-(6/3)*x = -8
-2*x = -8
x = -8/-2 = 4
We found the value of x, now we can replace this in one of the two equations to get the value of y.
Let's use the first equation:
y = -(1/3)*4 + 5 = -4/3 + 5 = -4/3 + 15/3 = (15 - 4)/3 = 11/3
Then the solution of the sytem is x = 4, y = 11/3.
Also can be written as (4, 11/3).