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Comment on 2 Equations with 2 Unknowns
To solve these equations by
Not necessarily. In some
Not necessarily. In some cases, the same strategies might apply.
For example:
3x² + y² = 20
2x² + 2y² = 4
Subtract bottom equation from top to get: x² = 16
So, x = 4 or -4
Hi, for the second example 3x
I believe you're referring to
I believe you're referring to the system that appears at 5:10 in the above video.
When it comes to the elimination method, there are infinitely many approaches we can take.
Our sole goal is to create EQUIVALENT equations that allow us to eliminate one of the variables.
So, your suggested approach will also work.
We have:
3x + 2y = 9
6x + 5y = 15
Take top equation and multiply both sides by -2 to get the following EQUIVALENT equation:
-6x - 4y = -18
6x + 5y = 15
Now ADD the two equations to get: y = -3
Once we know the value of y, we can determine that x = 5
So, the solution is x = 5 and y = -3 (just like in the video :-)
Cheers,
Brent
https://gre.myprepclub.com/forum
Can you solve this using substitution method by plugging in x=-10+y into the first algebra expression. If yes,please solve in detail.
Question link: https:/
Question link: https://gre.myprepclub.com/forum/if-x2-2xy-84-and-x-y-10-what-is-the-val...
Great idea.
Here's a solution that uses substitution: https://gre.myprepclub.com/forum/if-x2-2xy-84-and-x-y-10-what-is-the-val...
Cheers,
Brent
MPORTANT: (√a + √b)(√a - √b)
In your solution, you wrote:
-------------------------------
IMPORTANT: (√a + √b)(√a - √b) = a - b [this is a cute version of difference of squares]
We're told that a - b = 16 AND √a + √b = 8
Plug these values into the equation to get: (8)(√a - √b) = 16
From this, we can see that √a - √b = 2
We have:
√a + √b = 8
√a - √b = 2
When we ADD the two equations, we get: 2√a = 10, which means √a = 5
When we SUBTRACT the bottom equation from the top, we get: 2√b = 6, which means √b = 3
So, √(ab) = (√a)(√b) = (5)(3) = 15
Answer: E
We're told that a - b = 16 AND √a + √b = 8
Plug these values into the equation to get: (8)(√a - √b) = 16
-----------------------------------
I did not get how (√a - √b) = 16?
Question link: https:/
Question link: https://gre.myprepclub.com/forum/if-a-b-16-and-5652.html
My solution: https://gre.myprepclub.com/forum/if-a-b-16-and-5652.html#p10198
GIVEN a - b = 16 and √a + √b = 8
We know that: (√a + √b)(√a - √b) = a - b
Now use the GIVEN information (above) to replace a - b and √a + √b with their equivalent values.
We get: (8)(√a - √b) = 16
Does that help?
Cheers,
Brent