Question

How many solutions are there for the system of equations shown on the graph?

A coordinate plane is shown with two lines graphed. One line crosses the y axis at 3 and has a slope of negative 1. The other line crosses the y axis at 3 and has a slope of two thirds.

Answer 1

One solution

Explanation:

we know that

The solution of the system of equations is equal to the intersection point both graphs

we have

`y=-x+3` ------> equation A

`y=-(2/3)x+3` ------> equation B

Using a graphing tool

see the attached figure to better understand the problem

In this problem the intersection point is only one

therefore

The system of equations has one solution

The solution is the point
`(0,3)`

Answer 2

Only one solution

Explanation:

Given that there is a coordinate plane (say xy)

Two lines are given.

One line crosses the y axis at 3 and has a slope of negative 1.

hence equation of I line is y = -x+3

The other line crosses the y axis at 3 and has a slope of two thirds.

So equation is y = 2x/3 +3

Since the two lines lie in the same plane and are having different slopes, they intersect at one point.

Eliminate y to get

-x+3=2x/3+3

Or x=0

y=3

Hence solutionis (0,3) for the system.