# Write Word Problems into Systems of Linear Equations

Video solutions to help Grade 8 students write word problems into systems of linear equations and solve systems of linear equations using elimination and substitution methods.

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Lessons for Grade 8
Common Core For Grade 8
## New York State Common Core Math Module 4, Grade 8, Lesson 29

Lesson 29 Student Outcomes
• Students write word problems into systems of linear equations.

• Students solve systems of linear equations using elimination and substitution methods.

Lesson 29 Student Summary
• We know how to write information from word problems into a system of linear equations.

• We can solve systems of linear equations using the elimination and substitution methods.

• When we solve a system we must clearly define the variables we intend to use, consider which method for
solving the system would be most efficient, check our answer and think about what it means in context.
Finally, we should check to make sure we have answered the question posed in the problem.

Lesson 29 Classwork
Example 1

The sum of two numbers is 361 and the difference between the two numbers is 173. What are the two numbers?

Example 2

There are 356 Grade 8 students at Euclid's Middle School. Thirty-four more than four times the number of girls is equal
to half the number of boys. How many boys are in Grade 8 at Euclid's Middle School? How many girls?

Example 3

A family member has some five-dollar bills and one-dollar bills in their wallet. Altogether she has 18 bills and a total of
$62. How many of each bill does she have?

Example 4

A friend bought 2 boxes of pencils and 8 notebooks for school and it cost him $11. He went back to the store the same
day to buy school supplies for his younger brother. He spent $11.25 on 3 boxes of pencils and 5 notebooks. How much
would notebooks cost?

Exercises

1. A farm raises cows and chickens. The farmer has a total of 42 animals. One day he counts the legs of all of his
animals and realizes he has a total of 114. How many cows does the farmer have? How many chickens?

2. The length of a rectangle is 4 times the width. The perimeter of the rectangle is 45 inches. What is the area of the
rectangle?

3. The sum of the measures of angles x and y is 127". If the measure of angle x is34° more than half the measure of angle y,
what is the measure of each angle?