# Thread: [SOLVED] Need help solving a system of equation

1. ## [SOLVED] Need help solving a system of equation

Trying to figure out how they are coming up with 2,3 and not 5,3
Thanks

4x+3y=17
2x+3y=13

2. Nevermind, rather than adding the bottom equation they subtracted it which makes it come out to 2,3

3. subtract the 2nd equation from the 1st

you'll get 2x = 4

after solving you'll get x= 2

and put the value of x in any of the above eqn you'll get y

4. 4x+3y=17
2x+3y=13
______________________________________________

4x+3y=17
(2x+3y=13) - multi ply by -2 to the x terms. Now add . . . .

4x + 3y = 17
-4x - 6y = -26
0 - 3y = -9

y =-9/-3 = 3

Next,

4x+3y=17
2x+3y=13, multiply by -1 to eliminate y terms,

4x +3y = 17
-2x - 3y = -13 then add,

?

5. Originally Posted by Rheanna
Nevermind, rather than adding the bottom equation they subtracted it which makes it come out to 2,3
Just a note: It should make no difference whether they add or substract the equations -- either way there is one unique solution.

If you choose to add them, you get:

$4x+3y+2x+3y=17+13 \Rightarrow 6x+6y = 30 \Rightarrow 6(x+y) = 6*5$ $\Rightarrow x+y = 5 \Rightarrow x = 5-y$

Now substitute that into either equation, let's say the first:

$4(5-y)+3y = 17 \Rightarrow 20-4y+3y=17\Rightarrow -y = -3 \Rightarrow y = 3 \Rightarrow x + 3 = 5$ $\Rightarrow \boxed{x=2, y=3}$