Graphing Problem

Question

Two linear equations are shown.

What is the solution to the system of equations?

Answer 1

Since the equations of the lines are given you can solve for the intersection point by using the substitution method to first solve for x.

There are two expressions that are both equal to y so those expressions must be equal to each other at the point of intersection.

(1/3)x + 2 = (4/3)x - 5

My suggestion is to multiply every term of that equation by 3 to clear the equation of fractions (multiplication property for equality):

x + 6 = 4x - 15

21 = 3x

x = 7

When x = 7:

y=1/3(7)+2 =7/3 + 6/3 = 13/3

So the point of intersection is (7,13/3).

Verify here:

desmos.com/calculator/dhak9qy4iq

When solving the equation, since both fractions have the same denominator, it is not really necessary to clear the equation of fractions, so you could solve like this:

2 + 5 = (4/3)x - (1/3)x

7 = (3/3)x

x=7

Answer 2

Suggest you draw the two graphs on a larger grid and locate the intersection point.