Level 7-8 Algebra - Simultaneous Equations

1. Which of the following equations means exactly the same as 2x + 3y = 13?

   • 4x + 6y = 26
   • 6x + 4y = 26
   • 6x + 6y = 26
   • 6x + 6y = 13

2. Which of the following equations means exactly the same as 7x - 5y = 17?

   • 12x - 12y = 51
   • 21x - 15y = 51
   • 21x + 15y = 51
   • 2x - 5y = 51

3. Equation 1 is 2x + 3y = 19. Equation 2 is 3x + 6y = 30. How would we 'balance' one of the terms?

   • Add the terms in Equation 1 to the terms in Equation 2
   • Deduct the terms in Equation 1 from Equation 2
   • Multiply the terms in Equation 1 by 2
   • Multiply the terms in Equation 2 by 2

4. Equation 1 is 8x - 3y = 17. Equation 2 is 4x + y = 21. How would we 'balance' one of the terms?

   • Add the terms in Equation 1 to the terms in Equation 2
   • Deduct the terms in Equation 1 from Equation 2
   • Multiply the terms in Equation 1 by 2
   • Multiply the terms in Equation 2 by 2

5. We have balanced the y terms in two equations as follows: Equation 1 is 3x + 6y = 30 and Equation 2 is 4x + 6y = 38. What do we now do with them?

   • Add the terms in Equation 1 to the terms in Equation 2
   • Take the terms in Equation 1 from the terms in Equation 2
   • Divide Equation 1 by Equation 2
   • Multiply Equation 1 by Equation 2

6. We have balanced the x terms in two equations as follows: Equation 1 is 8x - 3y = 17 and Equation 2 is 8x + 2y = 42. What do we now do with them?

   • Take the terms in Equation 1 from the terms in Equation 2
   • Add the terms in Equation 1 to the terms in Equation 2
   • Divide Equation 1 by Equation 2
   • Multiply Equation 1 by Equation 2

7. By adding (or subtracting) one equation from another we have concluded that x has a value of 8 in the equation 3x + 6y = 30. What is the value for y?

   • 1
   • 2
   • 3
   • 4

8. By adding (or subtracting) one equation from another we have concluded that y has a value of 5 in the equation 8x - 3y = 17. What is the value for x?

   • 2
   • 4
   • 6
   • 8

9. What are the values of x and y that can be derived from the following simultaneous equations: 8x - y = 13 and 12x - 3y = 15?

   • x = 2 and y = 2
   • x = 2 and y = 3
   • x = 3 and y = 2
   • x = 3 and y = 3

10. What are the values of x and y that can be derived from the following simultaneous equations: 3x + y = 32 and 4x - 2y = 6?

    • x = 5 and y = 12
    • x = 6 and y = 10
    • x = 7 and y = 11
    • x = 8 and y = 6

Quiz written by Colin King