What is the most optimal way of solving these kinds of problems? 3x - 2y = 5 4x + y = 14 https://i.imgur.com/puhf2Vo.png

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What is the most optimal way of solving these kinds of problems? 3x - 2y = 5 4x + y = 14 https://i.imgur.com/puhf2Vo.png

Mathematics
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Originally I thought there was an ordered pair or 5, 5, but that won't work for the second equation.
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.
3x - 2y = 5 8x + 2y = 28 then we add them to be 11x + 0y =33

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you don't have to write 0y just 11x = 33 and then divide 11 on both sides.
That gives me x = 3, but that wouldn't be an ordered pair. Entering that back into the original equations won't work.
did you solve for y?
4x + y = 14 plug x = 3 back in this equation and solve for y
12 + y = 14 -12 on both sides y = 2 okay, then the pair is 3,2.
because right now you have (3, ?) we need y ... yes (3,2)
That still doesn't work if you put them into 3x-2y = 5.
not true 3(3) - 2(2) = 5 9-4=5 5=5
4x + y = 14 4(3)+2=14 12+2=14 14=14 it works
oh wait, I accidentally put in 3(2) and - 2(3)
You're correct, I'm, just a doof.
take a break from math... that's where mistakes pop up... by over doing them.
I'm gonna do that now, thanks for all the help! :)

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