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mathematics UK Year 10 Mathematics (KS4)
 
Solved problems for the chapter:
 

Simultaneous equations

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Solving linear equations and systems of equations for KS4
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:simultaneous_equations/3551/


Example 1.

The sum of two numbers is and their differences is . What are the numbers?

    
Example 2.

Solve the simultaneous equations using substitution method:




    
3.

Anja sells candy and cookies in her pastry shop. She sold a total of 40 products in one day. The price of the candy is 2 EUR each, and the price of the cookie is 4 EUR each. She earned € 100 that day. How many candies and how many cookies did she sell?

    
4.

Solves the simultaneous equation using substitution method:




    
5.

Solve the simultaneous equations:




    
6.

Three times a certain number is equal to twice the another number. The sum of the first number and the twice of the second number is equal to . Write down the numbers.

    
7.

Solve the simultaneous equations using elimination method:




    
8.

Solves the simulation equations using substitution method:




    

9.

Solves the simultaneous equations using substitution method:




    
10.

The number a is one greater than the number b. The difference between twice the number a and b is . Find the numbers.

    
11.

Solve the simultaneous equations using substitution method:




    
12.

Solve the system of equations using elimination method:




    
13.

Solve the simultaneous equations using elimination method:




    
14.

How many solutions does the following system of equations have?




    
15.

Solve the simultaneous equations using elimination method:




    
16.

Solve the simultaneous equations using elimination method:




    
17.

How many possible solutions are there for these simultaneous equations?




    
18.

How many solutions does these simultaneous equations have?




    

19.

The following line equations are given:






calculate the point of their intersection.

    
20.

Solves the simultaneous equations using substitution method:




    
21.

Solves the simultaneous equations using substitution method:




    
22.

Solve the simultaneous equations using elimination method:




    
23.

Solve the simultaneous equations using elimination method:




    
24.

Solve the system of two equations with two unknowns:




    
25.

Solve the system of two equations with two unknowns:




    
26.

Solve the system of two equations with two unknowns:




    
27.

Solve the system of two equations with two unknowns:




    
28.

Solve a system of two equations with two unknowns:




    

29.

Solve a system of two equations with two unknowns:




    
30.

Solve a system of two equations with two unknowns:




    
31.

Solve a system of two equations with two unknowns:




    
32.

Solve the system of two equations with two unknowns:




    
33.

Solve the system of two equations with two unknowns:




    
34.

Solve the system of two equations with two unknowns (leave your answer in terms of a):




    
35.

For which rational number a and b is and the solution of the set of equations below?




    
36.

Solve a system of two equations with two unknowns:




    
37.

Solve the systems of equations:






    
38.

Solve the systems of equations:






    

39.

Solve the systems of equations:






    
40.

Solve a system of linear equations with unknowns x and y:


    
41.

Solve the system of equations:




    
42.

Solve the system of linear equations:




    
43.

Solve a system of two linear equations with two unknowns:




    
44.

Solve the system of equations: