Solving Systems of Linear Equations by Graphing

Question

You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject? Use a system of linear equations to justify your answer.

Answer 1

If we let m represent the number of math problems and s represent the number of science problems, then we can write the following equation to represent the total number of question:

m + s = 42

Since you have 10 more math than science questions, we can also write that the number of math questions is 10 + s

If we substitute 10 + s into our equation for m, then we have:

10 + s + s = 42

Now we can solve for s by combining like terms and using inverse operations:

10 + s + s = 42

10 + 2s = 42

10 + 2s - 10 = 42- 10

2s = 32

2s/2 = 32/2

s= 16 science questions

The number of math questions will be 42 -16 or 26 math questions.