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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

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  1. anonymous
    • one year ago
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    Did you graph these or attempt to solve the system?

  2. anonymous
    • one year ago
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    I tried

  3. anonymous
    • one year ago
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    what did you get?

  4. anonymous
    • one year ago
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    two solutions

  5. mathstudent55
    • one year ago
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    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
    • one year ago
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    theres infinite solutions

  7. mathstudent55
    • one year ago
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    |dw:1441046418758:dw|

  8. anonymous
    • one year ago
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    how do i graph the numbers

  9. mathstudent55
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    theres infinite solutions

  12. mathstudent55
    • one year ago
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    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
    • one year ago
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    no solutions

  14. mathstudent55
    • one year ago
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    Correct.

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