Linear Combinations
The linear combinations method (also known as elimination) solves equations by eliminating variables so that each variable is solved individually.
| 1.) The
first step of the linear combinations method is to
multiply one or both of the equations by a constant
to obtain coefficients that differ in only one sign for
one variable (which will be eliminated). (Equation A is multiplied by -2 so that the coefficients of x in equation B and the revised equation A will have opposite signs.) |
Original Equations:
Equation A multiplied:
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| 2.) Next, simply add the revised equations to solve for the remaining variable (y). |
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| 3.)
Substitute the value of y into one of the original
equations to determine x. ( y is replaced with -6 in equation A, and then solved for x.) |
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| The solution to this system of equations is written as (-11/2, -6). |