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
- 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