Maria had x mistakes and Jose had y mistakes. The problem provides two conditions: y = x - 6, and 2x = 5 + 3y. Solving this system of two equations simultaneously reveals that Maria had 8 mistakes and Jose had 2 mistakes.

1. SYSTEMS OF LINEAR EQUATIONS
AND INEQUALITIES
Week 05: Solving Word Problems
Prepared by: Jojo M. Lucion
DISCUSSION
When you solve word problems you have to translate from English into mathematical sentences
and phrases. When a word problem involves two conditions, we may be able to translate each condition
into an equation. The numbers that satisfy both equations at the same time represent the solution of
the word problem.
A. Number Relation Problems
Example 1
In the recent achievement test Jose has 6 fewer mistakes than Maria. Twice the number Maria's
mistakes is 5 more than three times the number Jose has. How many mistakes does each have?
Let x = the number of mistakes Maria has
y = the number of mistakes Jose has

4. Solve for u
t+u=6
2+u=6
u=6-2
B. Business and Investment Problems

5. C. Geometric Problems

6. D. Motion Problems