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