Question

How do you solve a system of linear equations??

Answer 1

I like to subtract multiples of the equations to solve for one of the variables, then back substitute.

Answer 2

Okay I have an example can you show me how to do it? y=2x+6 and 4x-2y=13

Answer 3

it's in my math book. umm,

Answer 4

ok umm, i'll do the second one for you.
4x-2y=13
4x=15y
x=15y/4

Answer 5

i think that's right

Answer 6

Well here let me type it the right way I gues
y=2x+6
4x-2y=13

now is that easier??

Answer 7

umm that's the same as before.

Answer 8

I know but it's grouped together how do they work together or correlate?

Answer 9

Certainly.
\[y=2x+6\implies 2y = 4x + 12 \implies -4x + 2y = 12\]
Since we have another equation with a -2y we can just add the left and right sides of both equations together
\(-4x+2y=12\)
+\(4x-2y=13\)
\[\implies 0 = 25\]
So there is no solution.

Answer 10

Thankyou sooo much!! I'm gonna work on another problem like that one and I need you to see if I'm right okay?

Answer 11

Certainly.

Answer 12

You can actually note that those two equations have no solution because the lines are parallel so they'll never cross eachother. That's what you're finding when you solve these systems is where the graphs intersect.

Answer 13

Ohh! Okay I gotcha now that makes more sence.

Answer 14

Now I'm officially lost on this equation:
4x+2y=-10
-6x-2y=12 anad I got -2x+y=2 ;what do I do from there??

Answer 15

So close! But 2y -2y = 0 not y

Answer 16

Well I know but I didnt know whether to put y or 0y...so do I keep going from there or??

Answer 17

0y is correct. but that's the same as 0 which is the same as not putting it at all.

Answer 18

So you have -2x = 2

Answer 19

What is x?

Answer 20

-1

Answer 21

So substitute that in for x in either one of your original equations to solve for y.

Answer 22

3, so the answer would be (-1,3)

Answer 23

Or would it be -3???

Answer 24

(-1,-3) is correct.

Answer 25

Alright. Well, thankyou so much for helping me!(: that makes way more sence now