Question

Solve using elimination:
-3x = 14 + 2y
3y − 8x = -21

Answer 1

@MagicallyFarting

Answer 2

Write the rwo equations as
\(ax + by = c\)
one above the other.

Answer 3

Here's the first equation in that form:
-3x - 2y = 14
Now do the same for the second equation and write it below the first one.

Answer 4

is it be 8x-3y=-21

Answer 5

@mathstudent55

Answer 6

Almost. You need to be careful with the signs.
3y − 8x = -21
is the same as
3y + (-8x) = -21
Notice that the -8x term is negative; it's really -8x, and the 3y term is positive, so it turns into
-8x + 3y = -21

Answer 7

Now we write the new equations one above the other and we are ready to start with the elimination method.

-3x - 2y = 14
-8x + 3y = -21

Answer 8

so what do i do now and i did :) write it in elimination method

Answer 9

@mathstudent55

Answer 10

The elimination method works by eliminating a variable. To do that, you need to add both equations and make sure that one variable adds to zero.

The variables we have now, -3x and -8x add to -11x, and -2y and 3y add to y. They don't eliminate by addition, so we first need to modify them to be able to eliminate one variable by addition.

Answer 11

that means its one whole equation like -11x+y=-21

Answer 12

No.
First, the numbers on the right would also have to be added, to give 14 + (-21) = -7, but it still wouldn't help becauyse you still have x and y in the equation. We need to eliminate one variable. This is how we do it.

Notice the first equation has -2y, and the second equation has 3y.
If we multiply the entire first equationn by 3, the y term will become -6y.
If we multiply the entire second equation by 2, the y term will become 6y.
-6y and 6y do add to zero, thus eliminating the y variable, so that's what we need to dodo.

Answer 13

so i got
9x-6y=42
-16x+6y=-42

Answer 14

Excellent.
If you line them up, you'll be able to add more easily because the x's and the y's will line up:

9x - 6y = 42
-16x + 6y = -42
---------------- add

Answer 15

i got -7x+y=0

Answer 16

they y's cancelled out

Answer 17

ok so it -7x=0

Answer 18

Canceling out means no y left. You have a y there.
Careful. We are trying to eliminate y.
-6y + 6y = 0

9x - 6y = 42
-16x + 6y = -42
---------------- add
-7x = 0

See, no y variable left.

Answer 19

You got it now. Now that we have no y, and a simple equation in x, you can solve
-7x = 0
for x.
Divide both sides by -7.

Answer 20

excellent explaining math student....I always have trouble explaining elimination problems to people

Answer 21

@texaschic101 Thanks.

Answer 22

x=0

Answer 23

Great. Now that we have a value for x, insert that x value into x in one of the original equations.

Answer 24

-3x = 14 + 2y
-3(0) = 14 + 2y
Now solve for y. First simplify the left side. Then subtract 14 from both sides.

Answer 25

i got -7

Answer 26

@mathstudent55

Answer 27

Excellent. You just solved a system of equations by the elimination method. Good job.

The solution is:
x = -7, y = 0

Answer 28

awh thanks do you mind helping me on a few other questions also

Answer 29

no problem. pls start a new post

Answer 30

i tagged you in it