Topic Review — Simultaneous Equations

Review Questions

1. Substitution method. Fluency

   1. Solve: y = x + 5   and   2x + y = 14
   2. Solve: y = 4x − 3   and   x + y = 12
   3. Solve: x = 3y   and   x + 2y = 15
   4. Rearrange then substitute:   x + y = 10   and   3x + 2y = 26

2. Elimination method. Fluency

   1. 5x + 2y = 21   and   3x + 2y = 13
   2. 4x − y = 9   and   2x + y = 9
   3. 3x + 4y = 22   and   x + 2y = 10
   4. 2x + 3y = 17   and   3x + 2y = 18

3. Choose your method and justify. Understanding

   1. y = 2x + 1   and   3x − y = 4   (State which method and why.)
   2. 5x + 3y = 28   and   5x − y = 8   (State which method and why.)
   3. Determine whether the system 3x + y = 7 and 6x + 2y = 10 has one solution, infinitely many solutions, or no solution. Explain your reasoning.

4. Interpreting and verifying solutions. Understanding

   1. Jackson says the solution to x + y = 8 and 2x − y = 4 is x = 4, y = 4. Verify whether he is correct. If not, find the correct solution.
   2. The point (2, 3) is claimed to lie on both y = 2x − 1 and x + y = 6. Check both equations. Is (2, 3) the solution?

5. Real-world simultaneous equations. Problem Solving

   1. Two numbers have a sum of 32 and a difference of 10. Find the two numbers.
   2. A school tuck shop sells pies for $4 and sandwiches for $3. On Tuesday, 55 items were sold for $190. How many pies and how many sandwiches were sold?
   3. A landscaper charges a fixed call-out fee plus an hourly rate. A 2-hour job costs $110 and a 5-hour job costs $200. Find the call-out fee and the hourly rate.
   4. A paddock contains sheep and chickens. There are 25 animals in total. If you count legs, there are 76 in total. How many sheep and how many chickens are there?
   5. The angles in a triangle are p°, q° and 50°. The angle p is twice the size of angle q. Find p and q.