Question

What is the value of the x variable in the solution to the following system of equations?
2x + 3y = 4
x - 2y = -5

@eSpeX

Answer 1

@cshalvey @robtobey

Answer 2

You can use elimination to quickly solve for 'x', however using substitution will work as well.

Answer 3

How would I do the elimination way?

Answer 4

Elimination involved "eliminating" one of the variables, in this case, y. So you multiply each equation by a number that will allow you to get the 'y' values equal.

Answer 5

multiply the second by -2 and add both equations

Answer 6

What do you get if you multiply the two 'y' coefficients together?

Answer 7

6y, right?

Answer 8

Right, so what would you need to multiply into equation 1 to have 6y and in equation 2 to get -6y?

Answer 9

I have no clue, this is confusing.

Answer 10

In equation 1, you have 3y, so you need to multiply by 2 to get 6y. You must multiply the entire equation to keep from changing it, so
(2)(2x+3y=4) => (2*2x)+(2*3y)=(2*4) to give you
4x+6y=8

You do the other one.

Answer 11

Do the same with multiplying by 2 ?

Answer 12

If 2 times the 'y' will give you a 6

Answer 13

Oh, ok. Maybe I should use 3 then.

Answer 14

Exactly, good job.

Answer 15

3x - 6y = -15

Answer 16

Excellent. Now you want to add these two equations together, so x+x, y+y, and total + total:
4x +6y = 8
3x -6y = -15

And your resulting equation will allow you to solve for 'x' and get the answer to this problem. :)

Answer 17

7x + 12y = -7 ?

Answer 18

@jim_thompson5910

Answer 19

6y + (-6y) is not 12y

Answer 20

Oh, I didn't notice it was -6y

Answer 21

Is the answer -1

Answer 22

x = -1, yep

Answer 23

use that to find y

Answer 24

All I needed was x.

Answer 25

But thanks.

Answer 26

oh true, but it doesn't hurt to find y (for practice)

Answer 27

True. I'll write it down and try it when I finish these next questions.