## anonymous one year ago A set of equations is given below: Equation C: y = 5x + 10 Equation D: y = 5x + 2 Which of the following best describes the solution to the given set of equations? One solution No solution Two solutions Infinitely many solutions

1. anonymous

Did you graph these or attempt to solve the system?

2. anonymous

I tried

3. anonymous

what did you get?

4. anonymous

two solutions

5. mathstudent55

The system of equations in this problem is made up of two linear equations. A linear equation has a graph which is a straight line. If you are given two equations, there are three possibilities. 1. The two equations are two lines that intersect at one point. In this case, there is one solution to the system of equations. 2. The two equations look like two different equations, but they really are a single equation. In this case, every point on the line is a solution, and there are an infinite number of solutions. 3. The two equations are different, and the lines they represent are parallel. In this case, since the lines never intersect, there is no solution.

6. anonymous

theres infinite solutions

7. mathstudent55

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8. anonymous

how do i graph the numbers

9. mathstudent55

Now we need to look at the two equations in this system and see if we can conclude which one of the three cases it is.

10. mathstudent55

When the equation of a line is written in the form $$y = mx + b$$ m is the slope, and b is the y-intercept. The slope is a measure of the inclination of the line. The y-intercept is the point on the y-axis where the line crosses the y-axis. Parallel lines have the same slope and different y-intercepts.

11. anonymous

theres infinite solutions

12. mathstudent55

Now look at your equations. $$\begin{cases} y = 5x + 10 \\ y = 5x + 2 \end{cases}$$ Notice that both equations are already written in the y = mx + b form. In addition, in both equations, m is the same, 5. Both equation have the same slope, 5. This means these two equation can only be parallel lines or the same line. We tell the difference by looking at the y-intercept. Since one equation has y-intercept 10, and the other equation has y-intercept 2, the equations are of different lines. That means they are parallel lines. How many solutions are there to a system of linear equation of parallel lines?

13. anonymous

no solutions

14. mathstudent55
15. mathstudent55

Correct.