00:01
Hello, this is a linear systems problem where we need to use the elimination method to solve it.
00:05
So we're looking for the x and y coordinate that makes both of these equations true at the same time.
00:12
And so when we're using elimination, we want to look at getting rid of one of our variables when we add these two equations together.
00:21
And then we'll be able to have one equation with one variable that we can actually solve.
00:26
When i look at the x's and the ys, i see that i've got negative 2y and plus 3 y.
00:31
So if i can get these two numbers to be opposite of each other right here, i can add those together and they will add up to zero.
00:39
So i'm going to get rid of the ys and a common multiple of negative two and three is going to be six.
00:48
So i'm going to make both of these equations.
00:51
I'm going to make the top one negative 6y and the bottom one positive 6y.
00:57
And i'm going to do that by taking the top equation.
01:00
I'm going to multiply everything by positive three.
01:03
And the bottom equation, i'm going to multiply by two, because three times negative two is six y, and two times three y is six y.
01:11
And when i add those together, they're going to disappear.
01:14
However, and the common mistake here is to forget to do this.
01:19
When we multiply an equation by three, we have to multiply every single term by three.
01:25
So three times three x, this is nine x, 3 times negative 2y is minus 6y equals 3 times 1 which is 3 and then on the bottom 2 times 8 x is 16x 2 times 3y is plus 6y and then 2 times 2 is 4.
01:45
Okay now now that we've got this we can eliminate a variable 9 plus 16 that's going to be 25x negative 6y plus 6y is 0 so this is equal to 7 and when we divide by 24 on both sides, we end up with a fraction, x is equal to 7 .25s.
02:04
We want to leave our answer as a fraction because that's going to give us an exact answer when we go back and find the y value.
02:12
So we can use any of these equations, any four of these equations to find y.
02:18
I'm going to use this bottom one here because the numbers are smaller and i don't have any negatives.
02:25
But it doesn't really matter which one you choose.
02:28
So i'm going to do eight times...