Show all of your working.
Give your solution in the form (x, y)
1. Solve each pair of simultaneous linear equations using the most appropriate method:
|a.||x + y = 4||b.||y + 2x = 7||c.||y − 5x − 1 = 0|
|x − y = 2||4x − y = 11||y + 2x − 8 = 0|
|d.||2y = 7 − 3x||e.||5y + 4x = 47||f.||7x − 5y = 45|
|3y = 2x + 4||y − 2x = -13||2x + 3y = 4|
|g.||3x − 4y = 7||h.||y = -2x + 7||i.||y + 6 = x|
|2x − y = 3||y = 4x − 11||2y + 3 = x|
|j.||3x + 6y = 18||k.||x = 3 + y||l.||y = x − 4|
|5x − y = 8||2x + 4y = 12||3x + 2y = 2|
|m.||x − 3y = 2||n.||3x − 4y = 19||o.||y = 7x + 4|
|2x + 3y = 7||2x + y = 9||y = 2x − 1|
2. Solve the following pairs of simultaneous equations:
|a.||y = x2||b.||y = x + 2||c.||x = y − 7|
|y = 5x − 4||x2 + y2 = 10||xy = -12|
|d.||y = 2x − 3||e.||xy = 6||f.||y = 2x2 + 5x + 4|
|x2 + y2 = 9||y = x − 5||y − 2x − 3 = 0|
|g.||y = x2 − 7x + 18||h.||x2 + y2 = 13||i.|
|y = 3x − 7||y = x + 1||y = x − 2|
|j.||x = y − 3||k.||8 − 3x + 2y = 0||l.||y = 24 + 2x − x2|
|y2 = 3x||y = 12 − 2x|
For each of the following word problems, write a pair of simultaneous equations and then solve them before writing your answer as a statement.
3. Six pies and sixteen cokes cost $44, and two pies and four cokes cost $12.
What is the cost of:
(a) One pie (b) One coke
4. The cost of developing 20 large photographs and 24 small photographs is $232. Twelve large photographs and 32 small photographs cost $192. What would be the cost of developing:
(a) One large photograph
(b) One small photograph
5. Five CDs and two tapes cost $196.
Three CDs and one tape costs $114.
Find the cost of three CDs and four tapes.
6. The sum of two numbers is 112 and their difference is 36. Find the numbers .
7. Three pavlovas and two crayfish cost $72 and six pavlovas and five crayfish cost $168.
Find the cost of a crayfish.
8. 8 kg of bananas and 12 kiwifruit cost $22.00.
Four kiwifruit and 12 kg of bananas cost $26.00.
Find the cost of each kiwifruit and each kg of bananas.
9. The sum of two numbers is 168 and the difference between them is 32.
What are the numbers?
10. I think of a number and square it. The result is the same as if I had multiplied the number by 6 and taken it away from 16.
What is the number?