Mr. McKay wrote an algebra test with a total of 15 questions consisting of multiple choice and short response style questions. Multiple choice questions, x, were worth 5 points each and short response questions, y, were worth 10 points each. There were 100 total possible points on the test. Write and graph a system of linear equations for this situation to determine the number of each type of question.

Question

Mr. McKay wrote an algebra test with a total of 15 questions consisting of multiple choice and short response style questions. Multiple choice questions, x, were worth 5 points each and short response questions, y, were worth 10 points each. There were 100 total possible points on the test. Write and graph a system of linear equations for this situation to determine the number of each type of question.

Answer 1

10y = 100 - 5x

Cannot graph on these posts.

Answer 2

To write and graph a system of linear equations for this situation, let's define some variables:

Let x be the number of multiple-choice questions.
Let y be the number of short response questions.

Now, let's create equations based on the given information:

1) The total number of questions is 15: x + y = 15.

2) Each multiple-choice question is worth 5 points, and each short response question is worth 10 points. The total possible points on the test are 100: 5x + 10y = 100.

Now we have a system of two linear equations:

x + y = 15 (Equation 1)
5x + 10y = 100 (Equation 2)

To graph this system of equations, we can first rewrite Equation 1 in terms of y:

y = 15 - x (Equation 3)

Now we can create a table of values for x and y using Equations 3 and 2, and then plot these points on a graph.

Table of values:
------------------------------
| x | y |
------------------------------
| 0 | 15 |
| 5 | 10 |
| 10 | 5 |
| 15 | 0 |
------------------------------

Plotting these points on a graph, with x on the x-axis and y on the y-axis, we get a line:

| *
15 | *
| *
10 | *
|
5 |
|
0 --------------------
0 5 10 15

This line represents Equation 3, and it intersects the x-axis at x = 15 and the y-axis at y = 15.

Another way to graphically solve this system is to plot the line of Equation 1, which would intersect the y-axis at 15 and the x-axis at 15.

The point of intersection represents the solution to the system of equations, which in this case is x = 15 and y = 0. This means that there are 15 multiple-choice questions and no short response questions in this particular test.

Note: The graph can be used to find different solutions to the system of equations. For example, if we move along the line, we can find other combinations of x and y that will satisfy both equations.