Question

unit 5 systems of linear equations test

Answer 1

1. Solve the following system of equations using the substitution method:
2x + y = 10
x - 3y = 2

2. Solve the following system of equations using the elimination method:
3x + 2y = 11
2x - y = 3

3. Determine whether the following system of equations has one solution, no solution, or infinitely many solutions, and explain your reasoning:
x + 2y = 5
2x + 4y = 10

4. Solve the following system of equations graphically and state the solution:
3x + y = 6
x - y = 2

5. Solve the following system of equations using any method of your choice:
4x - 3y = 5
2x + 5y = 7

6. A system of linear equations can have more than two variables. True or false? Explain your reasoning.

7. Write a system of linear equations that has infinitely many solutions and explain why it has an infinite number of solutions.

8. Solve the following system of equations using the matrix method:
x + 2y = 7
3x - y = 5

9. What is the difference between consistent and inconsistent systems of linear equations?

10. Write a real-world scenario that can be modeled by a system of linear equations and solve it.