1.2.3 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