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 Question from marissa, a parent: Solve this linear system 2x-y=5 3x+y=-9

Marissa,

If 2x - y is 5 and 3x + y is -9 then their sum must be 5 + (-9) = -4. That is

(2x - y) + (3x + y) = 5 + (-9)

or simplifying

2x + 3x = -4

which is

5x = -4.

Thus

x = -4/5.

Substitute this value of x into the first equation, 2x - y = 5, to find y.

This is an example of one of the techniques used to solve linear systems. It's call the Method of Elimination. It worked nicely here because one equation contained y and the other contained -y so in their sum the y-terms were eliminated. Sometimes you need to manipulate the equations first to make the elimination work. For example to solve

2x - 3y = 4
x + 2y = 3

I would first multiply both sides of the second equation by 2 to obtain

2x - 3y = 4
2x + 4y = 6.

In this case if you subtract the second equation from the first you have

(2x - 3y) - (2x + 4y) = 4 - 6

or

-7y = -2

and hence

y = 2/7.

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.