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Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is worth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each point value are on the test.

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x - the number of 5 points worth problems
y - the number of 2 points worth problems

The test has 29 problems.
\(x+y=29\)

The test is worth 100 points.
\(5x+2y=100\)

The system of equations:
\(x+y=29 \\ 5x+2y=100\)

The solution:
\(x+y=29 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\times (-2) \\ 5x+2y=100 \\ \\ -2x-2y=-58 \\ \underline{5x+2y=100 \ \ \ \ \ } \\ 3x=42 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 3 \\ x=14 \\ \\ x+y=29 \\ 14+y=29 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |-14 \\ y=15\)

There are 14 problems worth 5 points and 15 problems worth 2 points.

There are 14 problems worth 5 points and 15 problems worth 2 points.

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Let x be the number of 5 points worth of problems

Let y be the number of 2 points worth problems

The test has 29 problems.

x + y = 29

The test is worth 100 points.

5x + 2y = 100

The solution are;

x + y = 29  

Or

-2x -2y = -59

5x + 2y = 100

By solving we get,

3x = 42

x = 14

and

y = 15

Hence, There are 14 problems worth 5 points and 15 problems worth 2 points.

Learn more about equations here;

https://brainly.com/question/10413253

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