System of Equations Word Problems
Solve real-world problems using systems of linear equations.
Includes
Standards
Topics
System of Equations Word Problems
Name:
Date:
Score:
Read each word problem carefully. Set up a system of two linear equations with two variables, then solve the system using substitution, elimination, or graphing. Show all your work.
1. The sum of two numbers is 50. Their difference is 10. What are the two numbers?
2. A cinema sold 500 tickets for a total of $4100. Adult tickets cost $10 and child tickets cost $7. How many adult tickets and child tickets were sold?
3. When solving a system of equations by substitution, you first solve one equation for one , then substitute that expression into the other equation.
4. If a system of equations has no solution, the lines are and will never intersect.
5. Which method is generally most efficient for solving a system of equations where one variable can be easily isolated?
Graphing
Substitution
Elimination
Matrix method
6. A farmer has chickens and cows. If there are 30 heads and 84 legs, how many chickens and how many cows does the farmer have?
7. You are selling tickets for a school play. Student tickets cost $5 and adult tickets cost $8. You sell a total of 150 tickets and collect $960. How many of each type of ticket did you sell?
8. When graphing a system of equations, the solution is the point where the lines intersect.
True
False
9. A system of equations with parallel lines has infinitely many solutions.
True
False
Related Worksheets
Finding Polynomial Functions from Graphs
This worksheet helps Grade 11 students practice identifying key features of polynomial graphs and using them to construct polynomial functions.
Radical Operations Worksheet
This worksheet provides practice on simplifying, adding, subtracting, multiplying, and dividing radical expressions for Grade 11 students.
Inductive Reasoning Worksheet
A Grade 11 math worksheet focusing on inductive reasoning, pattern recognition, and forming conjectures.
Conditional Statements Worksheet
Grade 11 Math worksheet focusing on conditional statements, converses, inverses, contrapositives, and biconditionals.
Solving Polynomial Equations Worksheet
Grade 11 Math worksheet focusing on solving polynomial equations, including factoring, rational root theorem, and synthetic division.
Introduction to Mathematical Proofs
This worksheet introduces grade 11 students to fundamental concepts and techniques in mathematical proofs, including direct proof, proof by contradiction, and propositional logic.
Grade 11 Matrices Worksheet
A worksheet for Grade 11 algebra students focusing on fundamental matrix operations, determinants, and inverses.
Properties of Equality Worksheet
Explore and apply the fundamental properties of equality including reflexive, symmetric, transitive, addition, subtraction, multiplication, and division properties with algebraic expressions.