Quadratic Simultaneous Equations (CIE A Level Maths: Pure 1)

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Quadratic Simultaneous Equations

What are quadratic simultaneous equations?

  • When you have more than one equation in more than one unknown, then you are dealing with simultaneous equations
  • An equation is quadratic if it contains terms of degree two, but no terms of any higher degrees (and also no unknowns raised to negative or fractional powers)

Quadratic and Non-quadratic, A Level & AS Level Pure Maths Revision Notes

 

  • Solving two simultaneous equations in two unknowns means finding pairs of values that make both of the equations true at the same time
    • At A level usually only one equation will be quadratic and the other will be linear
    • For one quadratic and one linear equation there will usually be two solution pairs (although there can be one, or none)

 

How do I solve quadratic simultaneous equations?

 

Step 1: Rearrange the linear equation so that one of the unknowns becomes the subject (if the linear equation is already in this form, you can skip to Step 2)

Step 2: Substitute the expression found in Step 1 into the quadratic equation

Step 3: Solve the new quadratic equation from Step 2 to find the values of the unknown (there will usually be two of these)

Step 4: Substitute the values from Step 3 into the rearranged equation from Step 1 to find the values of the other unknown

Step 5: Check your solutions by substituting the values for the two unknowns (one pair at a time!) into the original quadratic equation

Examiner Tip

  • You have to use substitution to solve quadratic simultaneous equations – the elimination method won't work.

Worked example

Quadratic Simultaneous Equations Example, A Level & AS Level Pure Maths Revision Notes

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Roger

Author: Roger

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.