Add the resulting equations if these equal coefficients have unlike signs; subtract one from the other if these equal coefficients have like signs.
It is generally best to select the letter to be eliminated which requires the smallest multipliers to make its coefficients equal; and the smallest multiplier for each equation is found by dividing the L. C. M. of the coefficients of this letter by the given coefficient in that equation. Thus, in example 2, the L. C. M. of and (the coefficients of ) is , and hence the smallest multipliers of the two equations are and , respectively.
Sometimes the solution is simplified by first adding the given equations, or by subtracting one from the other.
lint Ex. x + 49y = 51 (1) 49x + 49yy = 99 (2) [1] lint Add (1) and (2), 50x + 50y = 150 (3) [1] lint Divide (3) by , x + y = 3. (4) [1] lint Subtract (4) from (1), 48y = 48. y = 1. [1] lint Subtract (4) from (2), 48x = 96. x = 2.
Exercise 65.
Solve by addition or subtraction:
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