How do solve the following linear system?: -4x-15y=-1 , -3x+7y=-1 ?

1 Answer
georgef
Jul 31, 2016

The same values of x and y must satisfy both equations

Explanation:

Probably the easiest way to solve this is to manipulate the equations to bring them to a more convenient form in which both have the same coefficient for x. Multiply the fist one by 3 and the second one by 4:

-12x-45y=-3
-12x+28y=-4

This system is equivalent to the given one. Now we subtract the second form the first, and we get:
-73y=1, and then y=-1/73. Now replacing the y value in either equation, say the first one, we have:

-12x-45*1/73=-3, so

-12x=-3+45/73 so

-12x=(-219+45)/73, and then

-12x=-174/73, and this results in

x=(-1/12) * (-174/73), and simplifying

x=29/146

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