Question

0.3x - 0.2y = 4 and 0.4 = 0.3 y= -1

Answer 1

What are we doing with these?

Answer 2

There might be one too many equal signs there. Did you copy the problem correctly?

Answer 3

Alright - so, to get started, first identify which variable would be easier to cancel by way of elimination. Unfortunately, with these, there is no variable that is easier to cancel than any other, so you can just pick one. I'm going to go with "y". So let's look at causing the y's to cancel.

0.4x + 0.3y = -1
0.3x - 0.2y = 4

Answer 4

ok i tried doing that but was more confused

Answer 5

Now, the full name for this way of solving the system is "Elimination by Addition" So what we're trying to do is make it so the "y" values have the same coefficient (number in front of them) by we want them to have opposite signs.

Answer 6

ok

Answer 7

So first, to make things easy, let's get rid of those decimals by multiplying both equations by 10.

10(0.4x + 0.3y = -1)
10(0.3x - 0.2y = 4)

Answer 8

That would leave us with:
4x + 3y = -10
3x - 2y = 40

Answer 9

From here, let's multiply the top equation by "-2" and the bottom equation by "3". This will cause the y variables to cancel when we add these two equations together.

Answer 10

4(-2)x + 3(-2)y = (-2)-10
3(3)x - 2(3)y = (3)40

Answer 11

-8x + -6y = 20
9x - 6y = 120

Answer 12

Now, we can add them together.

Answer 13

That would leave us with 1x=140

Answer 14

got that so far

Answer 15

So we found that x=140

Now, you can plug that value into either equation for the "x" and solve for "y"

Answer 16

so then y would be -230 over -6

Answer 17

taking 1st equation
0.4x + 0.3y = -1
0.4x = -0.3y - 1
x = -(0.3y + 1) / 0.4

now put this value in 2nd equation ...
0.3x - 0.2y = 4
[-0.3(0.3y+1)] / 0.4 - 0.2y = 4
-0.09y/0.4 - 0.3/0.4 -0.2y = 4
from this extract value of y then put in 1st eqn , u will get of 'x'

Answer 18

4(140)+3y=-10

560+3y=-10

3y=-570

y=-190

Answer 19

So the solution would be (140, -190)

Answer 20

ok thank you this help me out

Answer 21

Happy to help! :)

Answer 22

It's always a good gesture to give the helper a "Good Answer" medal to show your appreciation! :)

Answer 23

solution is (-4.15, 2.2)

Answer 24

I'm sorry about that. I found the mistake:

From here, let's multiply the top equation by "2" and the bottom equation by "3". This will cause the y variables to cancel when we add these two equations together.

4(2)x + 3(2)y = (2)-10
3(3)x - 2(3)y = (3)40

8x+6y=-20
9x-6y=120

So when we add them, we get:

17x=100

x=100/17

Then, to get "y" plug (100/17) in for "x" in either equation. We'll do it for both of them just to make sure we're right this time.

8(100/17)+6y=-20
800/17+6y=-20
6y=-1140/17
y=-190/17

If we plug our x value of 100/17 into the other equation we get:

9(100/17)-6y=120
900/17-6y=120
-6y=1140/17
y=-190/17

So we know we got the right answer this time. ;)

So the solution should be : (100/17, -190/17)

PS: You were right, that one was tricky!!