 Hong Kong
Stage 4 - Stage 5

# Linear modelling- Simultaneous Equations

## Interactive practice questions

A family owns two businesses that made a combined profit of $\$6$$6 million in the previous financial year, with business B making 22 times as much profit as business A. Let xx and yy be the profits ( in millions) of business A and business B respectively. a Use the fact that the two businesses made a combined profit of \6$$6 million to set up an equation involving $x$x and $y$y.

b

Use the fact that business B made $2$2 times as much as business A to set up another equation relating $x$x and $y$y.

c

Which of the following sets of graphs correctly depicts the two equations?

A

B

C

D
d

Use the graph to find business A's profit.

e

Use the graph to find business B's profit.

Easy
Approx 6 minutes

A cat moves down a path at $8$8 m/s. A dog begins moving down the same path from the same point at a speed of $11$11 m/s, but starts $1.5$1.5 seconds later.

Luke purchases $30$30 L of mixed leaded and unleaded petrol solution for mechanic works, which costs him a total of $\$103.20$$103.20. The price of leaded petrol is \3.54$$3.54/L, while the price of unleaded petrol is $\$2.942.94/L.

Let $x$x and $y$y be the number of litres of leaded and unleaded petrol that make up the solution respectively.

Two twin soccer players are having a contest over who will score the most goals in the season. The twins have scored a combined total of $34$34 goals so far over the season and twin A has scored $6$6 more goals than twin B.

Let $x$x and $y$y be the number of goals scored by twin A and twin B respectively.