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