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
