Linear Systems question - solve this system:

1/x + 3/y = 3/4

3/x - 2/y = 5/12

Polynomials question:

Divide 2x – 1 into 4x4 – 5x2 + 2x + 4.

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- Nov 11th 2008, 11:18 AM14041471urgent algebra help needed!
**Linear Systems question - solve this system:**

**1/x + 3/y = 3/4**

**3/x - 2/y = 5/12**

**Polynomials question:**

Divide 2x – 1 into 4x4 – 5x2 + 2x + 4. - Nov 11th 2008, 11:28 AMajj86
For the first question, multiply the first equation by -3 and then add it to the second equation:

-3(**1/x + 3/y = 3/4)**

**+ 3/x - 2/y = 5/12**

**-3/x - 9/y = -9/4**

**+3/x - 2/y = 5/12 Find a common**denominator for the right hand sides of the equations:

**-3/x - 9/y = -27/12**

**+3/x - 2/y = 5/12 Multiplied the right hand side of the top equation by 3/3, which is essentially multiplying by 1.**

**Now add them:**

**-11/y = -22/12**

**Cancel out the negatives and cross multiply to get:**

**12*11 = 22*y**

**132 = 22y**

**y = 6**

**Substitute this value back into this original equation:**

**3/x - 2/y = 5/12 to find x.**

**3/x - 2/6 = 5/12**

**3/x = 5/12 + 4/12 got a common denominator for the constants**

**3/x = 9/12**

**Cross Multiply:**

**3*12 = 9*x**

**36 = 9x**

**x = 4**

**For practice, Substitute the x and y values back into both of the original equations to show that they check out.** - Nov 11th 2008, 11:29 AMearboth
- Nov 11th 2008, 12:06 PMajj862nd question
For the polynomials question, you start by asking yourself how many times 2x can go into 4x^4. Well, it would be 2x^3, because 2x*2x^3 = 4x^4.

So you multiply (2x-1) by 2x^3 and subtract it from the entire above polynomial: Looks like:

2x^3(2x-1) = 4x^4 - 2x^3

Now, do: (4x^4 - 5x^2 + 2x + 4) - (4x^4 - 2x^3)

The polynomial now looks like:

ii) 2x^3 - 5x^2 + 2x + 4

We do the same thing as above, ask ourselves how many times 2x can go into 2x^3. it would be x^2 times, since 2x*x^2 = 2x^3

So you multiply (2x-1) by x^2 and subtract it from the second stage polynomial (ii) above:

(x^2)(2x-1) = 2x^3 - x^2

Now, do (2x^3 - 5x^2 + 2x + 4) - (2x^3 - x^2)

The polynomial now looks like:

(iii) -4x^2 + 2x + 4

We do the same, and se that 2x can go into -4x^2 a number of -2x times because 2x*-2x = -4x^2.

So, you multiply (2x-1) by -2x and subtract it from the third stage polynomial (iii)

-2x(2x - 1) = -4x^2 + 2x

Now, do (-4x^2 + 2x + 4) - (-4x^2 + 2x)

The polynomial now looks like:

(iv) 4

You can't divide 2x into 4 any further, so we are done. The ending form looks like:

(2x-1)(2x^3 + x^2 -2x) + 4

Expand this to check to see if you get the original polynomial at the beginning. Hope this helps