Lesson: 2 Equations with 2 Unknowns

Comment on 2 Equations with 2 Unknowns

To solve these equations by the methods shown, the variables can only have a power of 1 correct? If something were squared, we must resort to another method of solving?
greenlight-admin's picture

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 + 2y = 9, why can’t we multiply this by -2? Wouldn’t we get the same answer for x?
greenlight-admin's picture

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/if-x2-2xy-84-and-x-y-10-what-is-the-value-of-y-9749.html
Can you solve this using substitution method by plugging in x=-10+y into the first algebra expression. If yes,please solve in detail.
greenlight-admin's picture

The question link is https://gre.myprepclub.com/forum/if-a-b-16-and-5652.html

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?
greenlight-admin's picture

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

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