Identifying the Number of Solutions

Examine the system of equations

-2x + 3y = 6

4x + y = 12

Answer the questions to determine the number of

solutions to the system of equations.

What is the slope of the first line?

What is the slope of the second line?

What is the y-intercept of the first line?

What is the y-intercept of the second line?

How many solutions does the system have?

Answer: 2/3, 2/3, 2, 2, Infinite

Explanation: I just finished the assignment

2/3 - 4 2 12 1

Step-by-step explanation:

For the line ax+by=c, solving for y gives ...

y = (-a/b) x + c/b

The slope in this slope-intercept form is the coefficient of x, - a/b. The y-intercept is c/b.

a) For the first line, the slope is ...

-a/b = - (-2) / 3 = 2/3

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b) For the second line, the slope is ...

-a/b = - 4/1 = - 4

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c) The y-intercept of the first line is ...

c/b = 6/3 = 2

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d) The y-intercept of the second line is ...

c/b = 12/1 = 12

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e) The slopes of the lines are different, so there is one (1) solution.