We are asked to solve via the elimination method the following system:
- x + 2 y = - 7
- 2 x + 3 y = - 1
so we pick to eliminate the term in x. and notice that in order to do that, we need to multiply the first equation by (-2) so our x term in it becomes "2 x" which is the exact OPPOSITE of the term "- 2 x " in the second equation.
Then we multiply the first equation by (-2) as shown below:
(-2) (- x + 2 y ) = (-2) ( - 7 )
2 x - 4 y = 14
now we combine term by term this transformed equation with the second equation in the system:
2 x - 4 y = 14
- 2 x + 3 y = - 1
____________
0 - 4 y + 3 y = 14 - 1
- y = 13
divide bith sides by (-1) to isolate y completely
y = 13 / (-1)
y = -13
Now we use this result in the original first equation to solve for x:
- x + 2 y = - 7
- x + 2 (-13) = - 7
- x - 26 = -7
add 26 to both sides
- x = 26 - 7
- x = 19
divide both sides by (-1) to isolate x completely
x = 19 / (-1)
x = - 19
Then our answer is: x = -19 and y = -13 which makes the coordinate pair: (-19, -13)