Question

solving with elimination method. 4x-6y=3 6x-4y=-3

Answer 1

4x - 6y = 3
6x - 4y = -3

Okay, so this one isn't exactly reduceable, like the previous one.

Answer 2

Also the slopes are not the same, so this one definitely has a solution.

Answer 3

Basically, now it just comes down to which variable you want to eliminate. It doesn't matter which one you choose. As long as you choose one.

Answer 4

could you explain how we figure what numbers to use to eliminate the variable.

Answer 5

After you choose a variable, say x perhaps, you'll want to rewrite both equations such that the the coefficients of both for variable x are the same.

Answer 6

ok

Answer 7

The co-efficients being the values affront the variable.

Answer 8

In order to make coefficents 4 and 6 the same in both equations, we have to multiply both equations by an appropriate number.

Answer 9

so if we chose x we would use -4x and -6x right

Answer 10

Well not exactly. the coefficients must be the same. for example:

4x + 3y = 8
4x + 2y = 6

Notice that the coefficients of variable x for both equations are the same. This means we would be able to use elimination method to simply subtract the second equation from the first. Doing that would lead us to y = 2 since subtracting both equations would lead to elimination of the x variable.

Answer 11

Another example is:

7x + 4y = 3
3x - 4y = 7

Notice that this time, we have a situation where the coefficients of y are opposites of each other. So combining both equations would eliminate the y variable leaving us with

10x = 10 which further simplifies to x = 1

Answer 12

So when we eliminate variables we must manipulate the equations to get these type of forms.

Answer 13

So anyway, back to this particular problem. Here we have:

4x - 6y = 3
6x - 4y = -3

In this case, we don't have either of the sample cases I've shown above. Instead, we have to manipulate the equations to get what we want. In order to do that we have to do a couple of things:

1st: We have to find the LCM of 6 and 4
2nd: We have to multiply the first equation by the appropriate factor to get the LCM as the coefficient of variable x, then we have to multiply the second equation by the appropriate factor to get the same LCM as the coefficient of x.

Answer 14

In this case, the LCM of 4 and 6 is 12 since:

4 x 3 = 12
6 x 2 = 12

This means we have to:
Multiply the 1st equation by 3
Multiply the 2nd equation by 2

Answer 15

When we do that, we get:
12x - 18y = 9
12x - 8y = -6

Answer 16

Now we have what we want, which is a case where the coefficients of x match. In this case (as described above) we want to subtract the second equation from the first to eliminate x

Answer 17

And upon doing so, we get:
-26y = 15 which is the same as 26y = -15

Answer 18

Unfortunately, we will not get easy integer values for y. It will be a fraction upon solving for y:

26y = -15
y = -15/26

Answer 19

To find x, we will need to plug the value for y back into the original equation and afterwards, solve for x.

Answer 20

now to do that do we just redo everything we just did but with y?

Answer 21

We already found y. We have to find x now and I just explained how to find x.

Answer 22

ok it makes sense now sorry i meant x :)