Question

(I BEG U TUTORS HALP) the linear equation. Y= -1/3 x+5 is shown graphed. If it was combined with the equation y=5/3 x-3 to form a system what would be the solution to this system? Show how you arrived at your answer

Answer 1

Answer: the solution of the sytem is x = 4, y = 11/3.

Step-by-step 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).