Method 3: Solving simultaneous equations by elimination The elimination method involves subtracting or adding the equations to eliminate one of the unknowns.
The aim is to manipulate the two equations so that, when combined, either of the unknown terms (i.e. the x term or the y term) is eliminated.The resulting equation with just one unknown can then be solved.
Solving simultaneous equations using elimination Put both equations in the form where the variables are on the LHS and any constants on the RHS (e.g. ax + by = c ). Label both equations.
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We need the coeffi cient (number in front) of one of the variables to be the same in each equation, but they must be opposite signs (e.g. one equation has + 3x and the other has − 3x ). If this is not the case, multiply one or both of the equations by a suitable number to make this be the case. Don’t forget to multiply every term in the equation by this value.
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Add the resulting equations to give an equation with one unknown. Solve the equation with one unknown from step 3.
Substitute the solution from step 4 back into one of the original equations containing the two unknowns. This will reveal the second unknown.
Worked example 2 Solve the following pair of simultaneous equations using elimination. 2x + y = 22
Solution 2x + y = 22
4x + 9y = 30 2x + y = 22 4x + 9y = 30
−4x − 2y = −44 + 4x + 9y = 30
If we had graphed these two equations, we would have found their point of intersection to be at (12, − 2).