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.
Milo adds 2x + y = 11 and x - y = 1, and the y terms vanish like magic: 3x = 12. What is the solution (x, y)?
Bo's puzzle card has 4x + 3y = 29 and 2x + 3y = 19. Subtracting the second from the first gives 2x = 10. What is the solution (x, y)?
Jun subtracts 2x + 4y = 14 from 5x + 4y = 23 to clear y. What new equation does Jun get?
- 7x + 8y = 37
- 3x = 9
- 3x + 8y = 9
- 3x = 37
Kira doubles every part of x - 2y = 4, like doubling a recipe. Which equation does Kira get?
- 2x - 2y = 8
- x - 2y = 8
- 2x - 4y = 8
- 2x - 4y = 4
Milo multiplies both sides of 3x + 2y = 5 by 4. Which equation does Milo get?
- 12x + 2y = 20
- 12x + 8y = 5
- 3x + 2y = 20
- 12x + 8y = 20
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?
- no solution
- infinitely many solutions
- exactly one solution
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?
- no solution
- exactly one solution
- infinitely many solutions
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
Bo solves 3x + y = 6 and -3x - y = -6 by adding the equations. The new equation is 0 = 0. How many solutions does the system have?
- exactly one solution
- infinitely many solutions
- no 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
- no solution
- infinitely many solutions