**How many solutions does the following system have: 6x - 3y = 9 2x - y = 3?**

Explain how to determine the number of solutions without solving the system. Then apply elimination, and interpret the resulting equation.

Explain how to determine the number of solutions without solving the system. Then apply elimination, and interpret the resulting equation.

- Krissy
**Posts:**1391**Joined:**08 Apr 2009, 18:45

I am trying to solve this problem, but not sure where to start solving linear equations and inequalities

- Lore
**Posts:**1366**Joined:**08 Apr 2009, 18:45

First you have to simplify everything. So distribute the 9 to the 2x+8 and distribute the negative to x+5

You get: 18x+72= 20 - x - 5

Then you want to get all like terms on one side (x's on the left)

add x to each side and add like terms (20-5): 19x+72 = 15

Then subtract 72 from each side

19x=-57

Divide each side by 19

x= -57/19

You get: 18x+72= 20 - x - 5

Then you want to get all like terms on one side (x's on the left)

add x to each side and add like terms (20-5): 19x+72 = 15

Then subtract 72 from each side

19x=-57

Divide each side by 19

x= -57/19

- Mathilde
**Posts:**1346**Joined:**08 Apr 2009, 18:45

Please help and thankyou very much

- Dell
**Posts:**1383**Joined:**08 Apr 2009, 18:45

Hi,

In order to get a horizontal asymptote, the degree of the numerator and denominator must be the same. In this case, they are the same because both would have an x² term as their largest exponents.

When that is true, the value of horizontal asymptote is found by dividing the coefficients of those leading terms. The numerator would have a leading term of kx² over the denominator's leading coefficient of 14x². That means that:

kx²

------- = 2

14x²

Multiplying both sides by 14x² to eliminate the fraction, you get:

kx² = 2(14x²)

kx² = 28x²

k = 28

I hope that helps!! :-)

In order to get a horizontal asymptote, the degree of the numerator and denominator must be the same. In this case, they are the same because both would have an x² term as their largest exponents.

When that is true, the value of horizontal asymptote is found by dividing the coefficients of those leading terms. The numerator would have a leading term of kx² over the denominator's leading coefficient of 14x². That means that:

kx²

------- = 2

14x²

Multiplying both sides by 14x² to eliminate the fraction, you get:

kx² = 2(14x²)

kx² = 28x²

k = 28

I hope that helps!! :-)

- Soo
**Posts:**1350**Joined:**08 Apr 2009, 18:45

I'm trying to simplify this equation to then figure out my second derivative.

- Debbi
**Posts:**1410**Joined:**08 Apr 2009, 18:45

If you look really carefully, in the numerator you can factor out a (x^2 - 9)^2 - there's two in the first term of the numerator and there is a (x^2 - 9) listed twice in the second term. Factoring those and cancelling some in the denominator leaves you with:

(-2x -2xs) / (x^2 - 9)^2

(-2x -2xs) / (x^2 - 9)^2

- Rolland
**Posts:**1344**Joined:**08 Apr 2009, 18:45

- Dina
**Posts:**1440**Joined:**08 Apr 2009, 18:45

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