How do you solve using elimination of #2x+5y=17# and #6x-5y=-9#?

1 Answer
sente
Nov 5, 2015

Add the equations to eliminate y and solve for x, and then substitute back to solve for y

Explanation:

Starting with
#{(2x + 5y = 17), (6x - 5y = -9):}#

We wish to solve for one of the variables by eliminating the other with addition or subtraction.
Note that we have #5y# in the first equation and #-5y# in the second. This means we may eliminate the variable #y# without further manipulation (in a more complicated case, we may need to first multiply both sides of one of the equations by a constant).
To do this, we can add the second equation to the first.

#(2x + 5y) + (6x - 5y) = 17 + (-9)=> 8x = 8#

Dividing both sides by 8 gives #x = 1#.

Then we simply substitute our result for #x# into either of the original equations. For example, using the first one gives
#2(1) + 5y = 17 => 5y = 15 => y = 3#

So the solution is #{(x = 1), (y=3):}#

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