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Algebra 1 Unit 5 – Systems of Linear Equations
Systems of Equations Word Problems
Handout 5-2
Class examples
Translating to a system of two equations is often easier than trying to convert all the
information into one equation. If two variables are used, then two equations must be written
in order to have a unique solution.
Example 1:
The sum of two numbers is 115. The difference is 21. Find the numbers.
Example 2:
The difference of two numbers is 49. One half of the larger number plus one seventh of the
smaller number is 56. Find the numbers.
Example 3:
2 angles are complemetary. The difference of their measures is 34 degrees. Find the angle
measures in degrees.
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Algebra 1 Unit 5 – Systems of Linear Equations
Homework Problems
Solve the following problems using two equations with two unknowns. Show all steps
(remember: identify question to be answered, define the variables, write the equations, solve
the system, check, and write the answer in a sentence.)
1.
The sum of two numbers is 27. One number is 3 more than the other. Find the numbers.
2.
Find two numbers whose sum is 58 and whose difference is 16.
3.
The difference between two numbers is 16. Three times the larger number is seven times the
smaller. What are the numbers?
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Algebra 1 Unit 5 – Systems of Linear Equations
4.
Then sum of two numbers is 26.4. One is fives times the other. Find the numbers.
5.
The sum of two numbers is 92. One eighth of the first number plus one third of the second
number is 19. Find the numbers.
6.
The sum of the length and the width of a rectangle is 19 in. The length is one less than twice
the width. Find the length and the width of the rectangle.
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Algebra 1 Unit 5 – Systems of Linear Equations
7.
The perimeter of a rectangle is 48m. The width of the rectangle is 2 more than half the
length. Find the length and the width.
8.
Two angles are complementary. One angle is 42 degrees more than one half the measure of
the other angle. Find the angle measures.
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