AQA A Level Maths: Pure复习笔记2.3.1 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