Solve a system by adding or subtracting the equations
Grade 8 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
A puzzle on the board says 3x + y = 17 and 2x - y = 8. Ren adds the two equations and gets 5x = 25. What is the solution (x, y)?
Noah solves 3x + 2y = 16 and x + 2y = 8. Subtracting the second equation from the first gives 2x = 8. What is the solution (x, y)?
Tala takes x + y = 10 away from 4x + y = 22, and y disappears: 3x = 12. What is the solution (x, y)?
Zee adds x + 3y = 11 and 2x - 3y = 4 to clear y. What new equation does Zee get?
- -x + 6y = 7
- 3x + 6y = 15
- 3x = 15
- 3x = 7
Pia lines up 2x + 5y = 19 and 4x - 5y = 11, then adds the two equations, very neatly. What new equation does Pia get?
- 6x = 30
- 6x = 8
- -2x + 10y = 8
- 6x + 10y = 30
Noah solves x + y = 5 and x + y = 8 by subtracting the second from the first. The new equation is 0 = -3. How many solutions does the system have?
- exactly one solution
- no solution
- infinitely many solutions
Ren solves 2x - y = 4 and -2x + y = 3 by adding the equations. The new equation is 0 = 7. How many solutions does the system have?
- infinitely many solutions
- exactly one solution
- no solution
Esme solves x - 2y = 3 and -x + 2y = -3 by adding the equations. The new equation is 0 = 0. How many solutions does the system have?
- no solution
- infinitely many solutions
- exactly one solution
Tala solves x + 2y = 6 and x - 2y = 6 by subtracting the second from the first. The new equation is 4y = 0. How many solutions does the system have?
- exactly one solution
- infinitely many solutions
- no solution
Zee solves 3x + y = 6 and 3x - y = 6 by subtracting the second from the first. The new equation is 2y = 0. How many solutions does the system have?
- infinitely many solutions
- no solution
- exactly one solution