0:03 In order to solve a system of equations,
0:05 you could always stack the two
0:07 equations. And then you want to combine
0:10 the like terms here. But in the middle,
0:13 we get 3 yus 3 y. Those ones are just
0:16 going to cancel. And that's always what
0:18 you want. You want one of the letters to
0:20 disappear cuz then we're going to
0:25 combine 4 and 4. So 8x there and 9 and
0:29 15, 24 on the right side. And finally,
0:31 it's going to be 8 time what will give
0:35 you 24? So x right there got to be
0:37 three. And then we're done for that problem
0:42 there. Sometimes we have to solve for
0:45 both letters x and y. That's called an
0:47 ordered pair, but you still start the
0:50 same way. So in this case, once again,
0:52 these y's are going to cancel. Let's get
0:56 rid of them. And then we've got 3x + x.
1:00 That's just a 1 x there. So 4x and then
1:04 12 and 8 20 on the right side. But once
1:08 again, 4 * what will give us 20. So x
1:11 has to be 5. But because it's an
1:13 equation, you could get x by itself.
1:16 It's being multiplied by 4. So we'll do
1:19 the opposite. Divide by 4. These will
1:23 cancel. 20 / 4. That's another way to
1:25 get five.
1:28 Now, x is always the first number, so it
1:31 could be a or it could be b, but let's
1:33 get rid of c and d. Then you want to
1:36 plug x back into one of the equations.
1:38 But the bottom one's nice and easy. So,
1:42 let's do that one. If x is 5, then 5 +
1:45 what will give us 8? But as we could
1:48 see, y has to be three. So, that is the
1:51 correct y value or the second number
1:55 there. and that's x, that's y. Those
2:02 there. Sometimes they'll just give you
2:05 one of the answers here. y is -2. That's
2:08 the second number. Could be b or could
2:12 be c. Let's get rid of the other guys.
2:15 Now we want to plug it back in. So we'll
2:18 get 5 * -2 on the left side there.
2:21 That'll give us -10. And then we want to
2:24 find what x could we plug in here to
2:26 make the right side
2:30 -10. But if we did x is -3, that'll do
2:37 it cuz 2 * -3 -6 - 4. That does give
2:42 -10. So x is -3. That's always the first
2:45 number. And then we knew y was -2. They
2:47 just told us. So see that's got the
2:50 right stuff there.
2:51 And one last
2:54 one. Sometimes the variables don't
2:57 cancel right away, but imagine if this
3:00 one had a three. Then those would cancel
3:02 there. That's what we want. So we're
3:03 going to multiply the whole second
3:08 equation by 3. So just copy the top one.
3:16 And then 3 * 2x 6 x 3 * y 3 y. 3 * 5 15
3:19 there. But as we said, the y's are going
3:21 to cancel. That's what we want. And
3:25 combining like terms, we get 10 x 25 and
3:29 15, 40. But you know what to do. 10 *
3:34 what will give you 40? So x is four. And
3:37 that's all for that guy there. So if the
3:39 equations don't cancel initially, you
3:41 could always multiply by something and
3:43 then you could get them to
3:45 cancel. Here's a video on solving
3:47 equations if you want some more practice
3:50 with those. Let me know what questions
3:52 and issues you run into. We'll see you
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