Question

What is the most optimal way of solving these kinds of problems?

3x - 2y = 5
4x + y = 14

https://i.imgur.com/puhf2Vo.png

Answer 1

Originally I thought there was an ordered pair or 5, 5, but that won't work for the second equation.

Answer 2

3x - 2y = 5 -----(1)
4x + y = 14 -----(2)

We need to make the coefficients for any variable equal(x or y).

So, if we multiply equation (2) by 2 , then both equations will have same coefficients of y.

Then just add both equations.. and y will be eliminated and x can be found.

Answer 3

3x - 2y = 5
8x + 2y = 28
then we add them to be

11x + 0y =33

Answer 4

you don't have to write 0y

just 11x = 33
and then divide 11 on both sides.

Answer 5

That gives me x = 3, but that wouldn't be an ordered pair. Entering that back into the original equations won't work.

Answer 6

did you solve for y?

Answer 7

4x + y = 14
plug x = 3 back in this equation and solve for y

Answer 8

12 + y = 14
-12 on both sides
y = 2
okay, then the pair is
3,2.

Answer 9

because right now you have (3, ?) we need y ...
yes (3,2)

Answer 10

That still doesn't work if you put them into 3x-2y = 5.

Answer 11

not true
3(3) - 2(2) = 5
9-4=5
5=5

Answer 12

4x + y = 14
4(3)+2=14
12+2=14
14=14
it works

Answer 13

oh wait, I accidentally put in 3(2) and - 2(3)

Answer 14

You're correct, I'm, just a doof.

Answer 15

take a break from math... that's where mistakes pop up... by over doing them.

Answer 16

I'm gonna do that now, thanks for all the help! :)