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Edexcel GCSE Maths Simultaneous equations

Simultaneous equations

This page covers the following topics:

1. Linear simultaneous equations by elimination
2. Linear simultaneous equations by substitution

To solve a set of linear equations we find the values of their variables. To do this the method of elimination can be used. In this method first we get rid of one of our variables by adding or subtracting the linear equations from each other. The equations can be multiplied beforehand by scalars if necessary. Combining equations leaves a simpler equation used to find the variable that has been not eliminated. Once the variable is found, its value can be substituted into one of the initial equations to find the second missing variable.

Linear simultaneous equations by elimination

To solve a set of linear equations we find the values of their variables. To do this the method of subsitution can be used. In this method we take one of the equations and rearrange it to make one of the variables the subject of the equation. Substituting this expression for the unknown variable into the second equation gives an equation with just one variable. Then we can solve this equation and substitute its solution the into any of the initial equations to find the second unknown variable.

Linear simultaneous equations by substitution

1

Let x = 2 and y = 5. Which set of the following simultaneous equations do given x and y values solve?

A) 4x + 3 = 2y + 1 and 3x βˆ’ 3 = y βˆ’ 2
B) 4x + 2 = 2y + 1 and 3x βˆ’ 3 = y βˆ’ 2
C) 8x + 6 = 4y + 2 and 6x βˆ’ 6 = 2y βˆ’ 2

Let x = 2 and y = 5. Which set of the following simultaneous equations do given x and y values solve? 

A) 4x + 3 = 2y + 1 and 3x βˆ’ 3 = y βˆ’ 2 
B) 4x + 2 = 2y + 1 and 3x βˆ’ 3 = y βˆ’ 2 
C) 8x + 6 = 4y + 2 and 6x βˆ’ 6 = 2y βˆ’ 2

2

Which of the following values solve the following simultaneous equations?

6x + 2 = y βˆ’ 1
2x βˆ’ 1 = βˆ’y + (14/3)w

A) x = 2/3 and y = 5
B) x = 1/3 and y = 5
C) x = 2/3 and y = 10

Which of the following values solve the following simultaneous equations? 

6x + 2 = y βˆ’ 1 
2x βˆ’ 1 = βˆ’y + (14/3)w

A) x = 2/3 and y = 5 
B) x = 1/3 and y = 5 
C) x = 2/3 and y = 10

3

Solve the simultaneous equations by using elimination method.

4x + 2y = βˆ’7
12x βˆ’ y = 7

Solve the simultaneous equations by using elimination method. 

4x + 2y = βˆ’7 
12x βˆ’ y = 7

4

2 apples and 4 pears cost Β£2.20. 7 apples and 1 pear cost Β£1.85. Find the cost of an apple and the cost of a pear by using the method of elimination.

2 apples and 4 pears cost Β£2.20. 7 apples and 1 pear cost Β£1.85. Find the cost of an apple and the cost of a pear by using the method of elimination.

5

Let x = 2 and y = βˆ’1/4. Which set of simultaneous equations do this x and y solve?

A) 6x βˆ’ 2 = βˆ’8y + 3 and βˆ’2x + 10 = 8y + 10
B) 12x βˆ’ 10 = βˆ’9y + 6 and βˆ’x + 6 = 4y + 6
C) 6x βˆ’ 5 = βˆ’8y + 5 and βˆ’x + 6 = 4y + 5

Let x = 2 and y = βˆ’1/4. Which set of simultaneous equations do this x and y solve? 

A) 6x βˆ’ 2 = βˆ’8y + 3 and βˆ’2x + 10 = 8y + 10 
B) 12x βˆ’ 10 = βˆ’9y + 6 and βˆ’x + 6 = 4y + 6 
C) 6x βˆ’ 5 = βˆ’8y + 5 and βˆ’x + 6 = 4y + 5

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