Simultaneous Equations

Simultaneous Equations

introduction
Simultaneous equations can be used to solve everyday problems, especially those which may not be easy to think through without writing anything down. For example, one can calculate the best routes for his / her journey, by creating a mathematical expression that takes into account the distances and average speeds for various parts of thejourney. You can use equations to set different goals, such as to minimise
the time spent on a journey or to maximise speed. You can also use simultaneous equations to find out the best deal, best plan, decide on a loan when determining investment ventures, and when considering the relationship between the price of a commodity and the quantity of the commodity. In this topic, you will understand, form, and solve simultaneous equations.

Activity 10.0 (Work in groups)
Nahwera buys 2 kg of sugar and 3 bars of soap at a total cost Of UGX 13,000 and
Draru buys 3 kg of sugar and 2 bars of soap at a total cost of UGX 14,500.
(a) Form a system of equations from the scenario above and clearly define the
variables used.
(b) Present your work to the rest of the class.
10.1 Solving Simultaneous Equations using Substitution
The substitution method works on the idea of replacement of equivalent expressions.

Activity 10.1 (Work in groups)
You are given a system of equations below.

(a) You are required to choose one equation and isolate one variable. Write downy our outcome.
(b)Replace the equivalent of the isolated variable in the other equation and then solve.
(c) What is your outcome?
(d)What is the solution of the other variable?
(e)Describe to the class how you can check the correctness of the solutions.

Revision Questions:
I) In a supermarket, Ssuubi buys 3 kg of sugar and 2 bars of soap at UGX 18,500 Kwagala buys 1 kg of sugar and 4 bars of soap at UGX 19,500. Find the cost of 19 bars of soap.
2) From a school canteen, Wamala bought 3 samosas and 2 egg rolls at UGX 2,600 while Kayongo bought 4 samosas and 1 egg roll at UGX 1,800. Would you save more by buying only 5 samosas, instead of buying only 1 egg roll?
3) From a fuel station, Isiko bought 5 litres of diesel and 1 litre of engine oil at UGX
39,250. Anywar bought 7 litres of diesel and 2 litres of engine oil at UGX 60,200.
What is the total cost of 12 litres of diesel and 15 litres of engine oil?
4) The sum of two different numbers is 60, and the difference between 3 times the smaller of the two numbers and the larger one is 40. What is twice the larger number?
5) A block of mass 15 kg was made by mixing sand and cement in the ratio of 1:4 by mass. Another block of mass 20 kg was made by mixing sand and cement in the ratio of 2:3. Find the total amounts of sand and cement used.
6) The cost of 6 pencils and 5 rulers is UGX 8,000, while the cost of 7 pencils and
8 rulers is UGX 11,500. Calculate the cost of 14 similar books, whose each cost is
UGX 2,000 less than the cost of 7 rulers.
7) A customer has to pay UGX 500 more for a pen than for 2 pencils. He pays UGX
2,500 more for 3 pens than for 4 pencils. How many pens would he buy at the
same cost of 18 pencils?

Topic Summary
In this topic, you have learnt that:
1) Simultaneous equations can be solved using substitution, elimination, graphs and matrices.
2) Solving simultaneous equations should give a solution that satisfies the two or more equations being solved.