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How many solutions does the system of linear equations represented in the graph have?

Coordinate plane with one line that passes through the points 0 comma 3 and 3 comma 4 and another line that passes through the points 0 comma negative 2 and 3 comma negative 1.

One solution at (−2, 0)
One solution at (0, −2)
No solution
Infinitely many solutions

User Kenshi
by
7.7k points

2 Answers

5 votes

Answer:

No solutions

Explanation:

I got it right on the test

User Raul Ferreira
by
7.9k points
3 votes

Answer:

No solutions

Explanation:

Sorry to say, there are no solutions to this system of linear equations. A quick look at the attached graph will illustrate this conclusion. The two lines that go through the given points are parallel. They both have a slope of (1/3), with y-intercepts of 4 and -2.

Calculate the slopes of both lines:

Line A:

Point 1 (0,3)

Point 2 (3,4)

Rise = 4-3 = 1

Run = 3-0 = 3

Slope = Rise/Run = (1/3)

Line B:

Point 1 (0,-2)

Point 2 (3,-1)

Rise = -1-(-2) = 1

Run = 3-0 = 3

Slope = Rise/Run = (1/3)

Since the lines have the same slope, no more work is needed. They are parallel and will not intersect. Therefore, there are no solutions.

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If interested:

The y-intercept for each line can be found by using one of the points for each line in the equation y = mx + b, where m is the slope of (1/3) and b is the y-intercept.

Line 1: y = (1/3)x + b

3 = (1/3)*(0) + b for (0,3)

b = 3

Both lines have a slope of (1/3). They are parallel and will never meet, even though they have a lot in common.

Line 2: y = (1/3)x + b

-2 = (1/3)*(0) + b for (0,-2)

b = -2

How many solutions does the system of linear equations represented in the graph have-example-1
User John Rajan
by
7.4k points