Question

Does anyone know of a simpler way to solve the system the substitution method? The following is a problem I have on hand;
x-3y=-15
4y-6x=62

Answer 1

multiply the first equation by 6

add this to the second equation,

the x's will cancel out

Answer 2

So confirming it will look something like this? (6x)-3y=-15

Answer 3

You have to multiply the whole first equation by 6.

first rearrange the order like so (change the order of the second equation):
x - 3y = -15
-6x + 4y = 62

Now multiply everything in the first equation by 6, on both sides of the equals sign:

6 ( x - 3y = -15 )
-6x + 4y = 62

Answer 4

x-3y =-15 (1st Eqn)


6(x-3y) = 6(-15) (1st Eqn times 6)
=

Answer 5

That makes sense now AgentO... Now will this give me the answer for x or y?

Answer 6

It'll give you y, since it'll eliminate x.
6 ( x - 3y = -15 )
-6x + 4y = 62

becomes

6x - 18y = -90
-6x + 4y = 62

Now add the two equations together.

Answer 7

now when you say add the two equations together, how does that look?

Answer 8

[6x - 18y] = [-90]
{-6x + 4y} = {62}


[6x - 18y ]+{-6x + 4y } = [-90] +{62}
6x - 18y -6x + 4y = -90 + 62

Answer 9

so is the final answer is (6,2) ?

Answer 10

Adding them vertically is easier imo, since they're already lined up.

6x - 18y = -90
-6x + 4y = 62
--------------
0 - 14y = -28

Answer 11

That is easier, thx for the tip...

Answer 12

so you've got y=2 right,

Answer 13

sub this into the first equation to get x

Answer 14

So instead of it being x-3y=-15 it would be x-3(2)=-15 to get x?

Answer 15

correct ..

Answer 16

Got it... (-9,2) Thank you both for ur assistance. this was a big help.

Answer 17

that's it \[\boxed{\large\color{red}\checkmark}%unk\]

Answer 18

Awesome.

Answer 19

and you can always check your solution by subbing the solution into the original equations

x-3y=-15
4y-6x=62

(x,y)=(-9,2)

(-9)-3(2)=-15
4(2)-6(-9)=62

both these should be true

Answer 20

^ learning to check your solutions is a good idea. You never need anyone to check your work (on systems of equations) if you check your own answers.

Answer 21

that's a cool way to check ur work , thx for the tip.