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SAT Math 1.3 Numbers and Operations. x and y must be which of the following?
SAT Math 6.3 Algebra and Functions 212 Views
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Description:
SAT Math 6.3 Algebra and Functions
Transcript
- 00:02
And we're getting math-y with it...
- 00:04
x + y = 1
- 00:06
y + z = -4
- 00:09
x + z = -19
- 00:12
Using the above equations, what is the value of z?
Full Transcript
- 00:15
And here are the potential answers...
- 00:20
What we've got here is a system of 3 equations, and 3 variables to solve for.
- 00:26
The first equation is x + y = 1.
- 00:28
We can subtract x from both sides to get y = 1 - x.
- 00:33
Now, let's plug in what we know into the second equation, y + z = -4.
- 00:38
For example, we can subtract y from both sides to get z = -4 - y.
- 00:43
What do we do next?
- 00:46
Or, we can substitute y out of this equation.
- 00:48
Now we need to define x in terms of z.
- 00:51
Our last equation can help with that.
- 00:53
So, let's subtract z from both sides,
- 00:56
and we will see that x is equal to -19 - z.
- 01:01
Now we can just substitute x out of our previous equation.
- 01:04
First, we'll distribute the negative sign into the parentheses.
- 01:08
Then, we'll do it again for the second pair of parentheses.
- 01:11
Finally, we'll add z to both sides, and combine the constants.
- 01:16
After this, we'll divide both sides by 2, and find that z = -12.
- 01:21
So our answer is (A).
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