Solving linear systems? algebra 1

solve the linear system. write the answer as an ordered pair.
3x-2y=14
-6x+5y=32
show work for total points (:

multiply the first equation by 2
2(3x-2y=14)
-6x+5y=32

solve for y
-6x+5y=32
+6x-4y=28
y=60

"plug" y into one of the original equations, solve for x
3x-2(60)=14
3x-120=14

add 120 to both sides
3x=134

divide 3 from both sides
3x/3=134/3
x=44 2/3

(44 2/3, 60) OR (134/3, 60) either way is fine you can simplify the fraction

3x-2y=14 -6x+5y=32
3x=2y+14
x=(2/3)y+(14/3)

Plug this into the second equation and solve for y

-6*((2/3)y+(14/3))+5y=32

-4y-28+5y=32

y=60
plug back through to solve for x
x=(2/3)(60)+(14/3)
=(120/3)+(14/3)=134/3

as a pair (x,y) it is ((134/3),60)

3x -2y = 14
-6x+5y = 32

multiply the first equation by two:

6x -4y = 28

add the second equation:

-6x +5y = 32
------------------
y = 60

substitute y=60 back into each equation:

3x - 120 = 14; 3x = 134; x=44 2/3
-6x + 300 = 32; 268 = 6x; x=44 2/3

Since both solutions for x agree, we are confident we have the right answer:

(x, y) = (44 2/3, 60)