The Linear Combination Method
So the graphing and substitution methods aren't your fancy? fWell, you're in luck! dMaybe the linear combination AKA elimination method will work best for you!
The Steps:
| Step 1: vMultiply one or both of the equations by a constant to obtain coefficients that differ only in sign for one of the variables. |
| Step 2: dAdd the revised equations from Step 1. dCombining like terms will eliminate one of the variables. dSolve for the remaining variable. |
| Step 3: dSubstitute the value obtained in Step 2 into either of the original equations and solve for the other variable. |
Now let's try to solve a linear system using the linear combination method!
2x - 4y = 13 ddddddddEquation 1
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh hhhh4x - 5y = 8hhhhhhh d Equation 2
SOLUTION: 1. sMultiply the first equation by -2 so that the the x-coefficients differ only in sign. ssssssssssssss(-2)2x - 4y = 13 -------- -4x + 8y= -26 fffffffffffffffffffffffff 4x - 5y = 8 --------- 4x - 5y = 8 2. dAdd the revised equations and solve for y. frfffffffffffffffffffffffff 3y = -18 sssssssssssssffffffffffffy = -6 3. jSubstitute the value of y into one of the original equations. fSolve for x. sssddddddddddd 2x - 4y = 13ddddddddd Write equation 1. ssvvvvvvvvvv2x - 4(-6) = 13fffffffffffffff Substitute -6 for y. ddddddddddddd 2x + 24 = 13fffffffffffffff Simplify. fffffffffffffffffffffffff x = -11/2sssssssssssSolve for x.
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