### Spares are GREAT! Scribe Time

Today in class started off in the usual matter with Mr. K posting up three examples of Non-Linear Equations for us to solve:

1) 2x^{2} + y = 12

x + y -3 = 0

2) x + y = 5

x^{2} + y^{2} = 17

3) x^{2} + 4y^{2} = 49

2x^{2} - 3y^{2} = -12

Well we WERE supposed to solve these equations, but got distracted from the PILES of tests, pre tests and quizzes that Mr. K seemed to have forgotten to return to us, but it is all good at least we all know where we stand for first term =D. Also Mr. K gave us a lecture on how **NEXT TUESDAY IS THE LAST DAY TO MAKE UP MISSED WORK, WEDNESDAY IS TOO LATE!!** OH and also you have to give him a day advance so he could make up the test or what you have missed. This lecture led into what Mr. K believed what the marks on our tests and stuff reflect, but now what we have learned but how we apply ourselves, so like Mr. K said if you are doing bad like REALLY bad in class I think you should start applying yourself more. Anyway back to the real reason for this scribe.

Example 1:

2x^{2} + y = 1 L_{1}

2x + y -3 = 0 L_{2}

y = -2x + 3 L_{3}: Rewrite L_{2}

2x^{2} + (-2x+3) = 1 L_{4}: Sub L_{3} into L_{1}

2x^{2} - 2x + 2 = 0 L_{5}: Solve L_{4}

x^{2} - x + 1 = 0

Since it does not factor nicely we use the quadratic formula to solve for x. After doing so we find out that the parabola and the line do not intersect. Sorry I didn’t put in the quadratic formula don’t know how to put it in =/

Example 2

x + y = 1 L_{1}

x^{2} + y^{2} = 0 L_{2}

y = -x + 5 L_{3}: Rewrite L_{2}

x^{2} + (-x + 15)^{2} = 17 L_{4}: Sub L_{3} into L_{1}

x^{2} + x^{2} -10x +25 = 17 L_{5}: Solve L_{4}

2^{2}-10x+8 = 0

x^{2} - 5x + 4 = 0

(x - 4) (x -1) = 0

(4) + y = 5 L_{6}: Solve L_{1} w/ x = 4

y = 1

(1) + y = 4 L_{7}: Solve L_{1} w/ x = 1

y = 3

Therefore the line intersects the circle at (4,1) and (1,4)

Example 3

x^{2} + 4y^{2} = 49 L_{1}

2x^{2} - 3y^{2} = -12 L_{2}

11y^{2} = 110 L_{3}: 2L_{1} – L_{2}

y^{2} = 10 L_{4}: Solve L_{3}

*y^{2} - 10 = 0

*(y – root 10) (y + root 10) = 0

*y = root 10 y = - root 10

x^{2} + 4 (root 10) ^{2} = 49 L_{5}: Solve L_{1} w/ y = root 10

*x^{2} = 9

*x^{2} - 9 = 0

(x + 3) (x – 3) = 0

x = -3 x = 3

And if you do the same thing with – root 10 you get the same answer.Therefore making the Ellipse and Hyperbola intersect at four places (-3, root 10) and (3, root 10) twice.

After solving that equation MR. K went into explaining the difference of Ellipses and Hyperbola’s. Even though their equations may look the same, the positive y^{2} changes the equation from a circle to a ellipse and if it was negative from an ellipse to a hyperbola, but this is something we will we learning in our future studies of Pre-Cal 40S.

NOTE: * If you do this instead of squaring everything, this will make Mr. K glow like the sun =D. Ok exaggerated but he will be really, REALLY happy if you do.

And that was how class was today despite Mr. K yet again explaining how we are writing a text book so here’s the next page to the chapter of **Analytic Geometry**. Early scribe yes I know haha I have nothing else to do on my spares =/.

BTW Tomorrow's scribe is going to be aldridge, lol and sorry if the txt is TOO small i just don't like big txt.

## 2 Comments:

wow awesome scribe post Abriel, I can tell you took a lot of time doing that..good job!

I want a spare. Hahahaha

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