## Simultaneous Equations Exercise

Show all of your working.

Give your solution in the form (x, y)

1. Solve each pair of simultaneous equations using a graphical method:

 (a) x + y = 4 (b) y + 2x = 7 (c) y − 5x − 1 = 0 x − y = 2 4x − y = 11 y + 2x − 8 = 0

2. Solve each pair of simultaneous equations using the elimination method:

 (a) x + y = 4 (b) 5y + 4x = 47 (c) 7x − 5y = 45 x − y = 2 y − 2x = -13 2x + 3y = 4

3. Solve each pair of simultaneous equations using the comparison method:

 (a) y = 4 − x (b) y = -2x + 7 (c) y + 6 = x y = x − 2 y = 4x − 11 2y + 3 = x

4. Solve the following simultaneous equations using the substitution method:

 (a) y = x + 2 (b) x = 3 + y (c) y = x − 4 x + y = 4 2x + 4y = 12 3x + 2y = 2

5. Solve the following simultaneous equations:

 (a) x − 3y = 2 (b) 3x − 4y = 19 (c) y = 7x + 4 2x + 3y = 7 2x + y = 9 y = 2x − 1

6. Three pies and 8 milkshakes cost \$22, and one pie and two milkshakes cost \$6.

What is the cost of:

(a) One pie
(b) One milkshake

7. The cost of developing 10 large photographs and 12 small photographs is \$116. Six large photographs and 16 small photographs cost \$96. What would be the cost of developing:

(a) One large photograph
(b) One small photograph