Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Algebra - Equations - Simultaneous equations - Solve by graphing.
Test Yourself 1 - Solutions.


 

1.

POI is (-3, 1)

 2.

POI is (1, 2).
3.

POI is (1, -4).

 4.

POI is (1, -3).
5.

POI is (2, 6).

 6.

POI is (1, 0)

 

Use the following descriptions to develop two equations. Then graph the equations to solve them simultaneously:
7. Let the two numbers be x and y.

∴ x + y = 19

x - y = 5


So the numbers are 12 and 7.

8. Let the biscuits be b and the cakes be c.

Three biscuits and 4 cakes cost 55 cents.

So 3b + 4c = 55

... two biscuits and 5 cakes cost 60 cents.

2b + 5c = 60.

So the biscuits cost 5c
and the cakes cost 10c.
9. Let $S be the unit price of the steak and $B be the unit price of the sausages.

4S +2B = 136 (or you could simplify to 2S + B = 68)

S + 5B = 88

So steak cost $28/kg and sausages cost $12/kg.

 

Write the cost and revenue equations for each of the following situations and then graph the equations to answer the accompanying questions:
11. (i) After how many hours do Tom's income equal his costs?

Let cost be C, I be income and h be hours worked.

C = 135 + 35t

I = 50t

For breakeven, costs = income

135 + 35t = 50t

t = 9

So Tom must work for 9 hours to breakeven.

 (ii) What is Tom's financial position for the week if he works for 20 hours?

For 20 hours work:

Costs = 135 + 35 × 20 = $835

Income = 50 × 20 = $1,000

Profit = $165.