Linear Simultaneous Equations - Elimination (CIE A Level Maths: Pure 1)

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Linear Simultaneous Equations - Elimination

What are simultaneous linear equations?

  • When you have more than one equation in more than one unknown, then you are dealing with simultaneous equations
  • An equation is linear if none of the unknowns in it is raised to a power other than one
  • Solving a pair of simultaneous equations means finding pairs of values that make both equations true at the same time
  • A linear equation in two unknowns will produce a straight line if you graph it... linear = line
  • A pair of simultaneous equations will produce lines that will cross each other (if there is a solution!)

How do I use elimination to solve simultaneous linear equations?

Step 1: Multiply one (or both) of the equations by a constant (or constants) to get the numbers in front of one of the unknowns to match

Step 2: If the matching numbers have the same sign, then subtract one equation from the other. If the matching numbers have different signs then add the equations together

Step 3: Solve the new equation from Step 2 to find the value of one of the unknowns

Step 4: Substitute the value from Step 3 into one of the original equations, and solve to find the value of the other unknown

Step 5: Check your solution by substituting the values for the two unknowns into the original equation you didn't use in Step 4

Examiner Tip

  • Don't skip the checking step (it only takes a few seconds) – there are many places to go wrong when solving simultaneous equations!
  • Mishandling minus signs is probably the single biggest cause of student error in simultaneous equations questions

Worked example

2-3-1-linear-simult-eqns---elim-example-1

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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.