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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 $2$2 times as much profit as business A.

Let $x$x and $y$y be the profits ( in millions) of business A and business B respectively.


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.


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.


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

Loading Graph...


Loading Graph...


Loading Graph...


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Use the graph to find business A's profit.


Use the graph to find business B's profit.

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 $\$2.94$$2.94/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.

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