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OCR A-level Maths Simultaneous equations

Simultaneous equations

This page covers the following topics:

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

To solve a set of quadratic 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.

Quadratic simultaneous equations by elimination

To solve a set of quadratic 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.

Quadratic simultaneous equations by substitution

1

The graph represents the quadratic equations xΒ² + yΒ² = 4 and (x βˆ’ 5)Β² + yΒ² = 16. Find the exact coordinates of the points of intersection of the two graphs by using the elimination method.

The graph represents the quadratic equations xΒ² + yΒ² = 4 and (x βˆ’ 5)Β² + yΒ² = 16. Find the exact coordinates of the points of intersection of the two graphs by using the elimination method.

2

Use the method of substitution to solve the simultaneous equations provided.

3y + x = 19
2xΒ² + 3yΒ² = 146

Use the method of substitution to solve the simultaneous equations provided. 

3y + x = 19 
2xΒ² + 3yΒ² = 146

3

The diagram represents the graphs of xΒ² + yΒ² = 52 and y = βˆ’2x βˆ’ 8. Use the method of substitution to find the coordinates of the points of intersection.

The diagram represents the graphs of xΒ² + yΒ² = 52 and y = βˆ’2x βˆ’ 8. Use the method of substitution to find the coordinates of the points of intersection.

4

Use the elimination method to solve the following simultaneous equations.

11xΒ² βˆ’ 7y = 191
13xΒ² + 14y = 493

Use the elimination method to solve the following simultaneous equations. 

11xΒ² βˆ’ 7y = 191 
13xΒ² + 14y = 493

5

Solve the simultaneous equations provided by using the elimination method.

5xΒ² + 9y = 71
7xΒ² βˆ’ 3y = 115

Solve the simultaneous equations provided by using the elimination method. 

5xΒ² + 9y = 71 
7xΒ² βˆ’ 3y = 115

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