# StudySquare

# AQA GCSE Maths Simultaneous equations

This page covers the following topics:

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 get rid of one of our variables. This is done by adding or subtracting the linear equations from each other, the equations can be multiplied by scalars if necessary. Which leaves a simple equation to calculate the variable that has been not eliminated.

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 take one of the equations and simplify use addition and subtraction so that on one side of the equation only an unknown variable is left. Substitute this value for the unknown variable into the second equation, making sure that the unknown varible is multiplied correctly. Solve this simple linear equation with only one unknown variable and then substitute this solution into the into the equation for the other unknown varible to find the second unknown variable.

As with linear equations, two quadratic equations or a combination of one quadratic and one linear equation can also be solved simultaneously. One of the methods to do this is by elimination, which required adding or subtracting the equations (or multiples of them) to eliminate one of the variables.

Another method to solve quadratic equations simultaneously is through substitution. This can be done by rearranging one of the equations such that one of the variables can be written in terms of the other variable. This can then by substituted in the other equation and solve for the variable.

# 1

# ✅

Using the method of elimination solve the following simultaneous equations: 3x + 4 = 4y − 1 and 2x − 3 = 2y − 5.

# 2

# ✅

For the simultaneous equations 6x + 2 = y − 1 and 2x − 1 = −y + 14/3 which of the following values for x and y solve them?

A) x = 2/3 and y = 5

B) x = 1/3 and y = 5

C) x = 2/3 and y = 10

# 3

# ✅

Using the method of subsitution solve the simultaneous equations x + 4y = 9 and 2x + 2y = 6.

# 4

# ✅

Using the method of substitution solve the following simultaneous equations 4x − 5 = 2y − 7 and −2x + 3 = 3y − 4.

# 5

# ✅

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

A) 4x + 3 = 2y + 1 and 3x − 3 = y − 2

B) 4x + 2 = 2y + 1 and 3x − 3 = y − 2

C) 8x + 6 = 4y + 2 and 6x − 6 = 2y − 2.

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