Solve algebraically: 6x + y = 16, 5x - 2y = 19
The first step to eliminate one of the unknowns, in this case x or y. This can be done by making the coefficient (the number before) of one of the unkowns the same number, or the negative of the same number, in each equation.In this example, we can multiply the first equation by 2 to get:12x + 2y = 32So 2 is now the coefficient of y in one equation and -2 is in the other.We can now eliminate y by adding the equations together:12x + 2y = 32 5x - 2y = 19 + 17x = 51Now we can easily solve for x by dividing both sides of the equation by 17:x = 3Then to solve for y, all we have to do is substitute our value for x back into one of the original equations:6x + y = 16 6(3) + y = 16 18 + y = 16 y = -2(To check the answer, we can sub x and y back into the other equation: 5x - 2y = 5(3) - 2(-2) = 15 - (-4) = 19 which is correct!)
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