Algebra - Simultaneous equations - basic techniques.
Test Yourself 1.
Simultaneous equations using equations with 1 in front of one of the variables:
1. 2x - y = 3
Answer.x = 4 and y = 5 |
2. 8 = 3x + y
Answer.x = 1 and y = 5 |
3. x = 11 - 3y
Answer.x = 5 and y = 2 |
4. y = 2x + 1
Answer.x = -2 and y = -3 |
5. 2x - 3y = -1
Answer.x = 4 and y = 3 |
6. 5x + 2y = -8
Answer.x = 0 and y = -4 |
Simultaneous equations having equal coefficients for one variable:
7. 4a - 3b = 11
Answer.a = 2.6 and b = -0.2 |
8. 5e - 3f = 20
Answer.e = 5 and y = 5/3 |
9. 5p - q = 24
Answer.p = 7 and q = 11 |
10. 11a + 9b = 34
Answer.a = -1 and b = 5 |
11. 3y - 4x - 1 = 0
Answer.x = 2 and y = 3 |
12. 5p + q = 10
Answer.p = 1 and q = 5 |
Applied questions (mainly of the "break-even" type).
| 13. Two brothers Chuck and Dave drive vehicles between Sydney and Gunnedah - a distance of 430 kms. Chuck drives a truck which leaves Gunnedah at the same time as Dave leaves Sydney in his car.
Chuck drives the truck at an average speed of 60 kph while Dave drives his car at an average speed of 80 kph (its a sporty grey model). After what time will the brothers meet up to have a coffee and a talk? |
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14. A small end of Year 12 function is being organised. The Organising Committee needs to pay $280 to reserve a venue and has alloted $230 for advertising, insurance and purchase of basic decorations. The caterers change $25 per person for the light finger food. Tickets for the function are to be sold at $40 per person.
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