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Algebra Question

Factor, solve for x, then solve y. Its a system of equation, solution should work for both equations.
 
Since it's multiple choice, you can just plug in the values they give you for each answer choice and see which set works. Granted, this is not the "proper" way to solve the question but can possibly be faster than the factoring method.
 
x^2 + y^2 = 25 and x + y = 1
So, you want to isolate a variable here, where it's easier (no exponents):
x + y = 1
y -1 + x = 0
y -1 = -x
x = 1 - y
OK, now:
x^2 + y^2 = 25
(1 - y)^2 + y^2 = 25, so get (1-y)^2
(1 - y)(1 - y) + y^2 = 25
1 -2y + 2y^2 = 25
2y^2 -2y = 24
2y^2 -2y -24 = 0
Now it's a quadratic. You can figure that with the quadratic formula[1], or do a couple numbers in your head. Long story short:
2(4)^2 - 2(4) = 2(16) - 8 = 32 - 8 = 24.

OK, y = 4.
So,
y + x = 1
4 + x = 1
4 = 1 -x
3 = -x
-3 = x, and try it:
x^2 + y^2 = 25
(-3)^2 + (4)^2 = 25
9 + 16 = 25
25 = 25.
It works. Also, since the parts with x and y are the same, x and y can be either 4 or -3 at any time (-3^2 + 4^2 = 4^2 + -3^2).

[1] - I had to stop winamp so I could remember the song 🙂.
[-b +/- sqrt(b^2 - 4ac)] / 2a
 
Originally posted by: GiLtY
If you are pressed for time (like you are taking a SAT test), just plug the answers in.

--GiLtY
Click to expand...
On such a test, you can bring calculators that can also make that extremely fast. Unfortunately teachers tend to like work 🙂

-Ernie, who knows he's got to take Calc and Calc II in a semester or two.
 
Originally posted by: Cerb
Originally posted by: GiLtY
If you are pressed for time (like you are taking a SAT test), just plug the answers in.

--GiLtY
Click to expand...
On such a test, you can bring calculators that can also make that extremely fast. Unfortunately teachers tend to like work 🙂

-Ernie, who knows he's got to take Calc and Calc II in a semester or two.
Click to expand...

can a ti-85 do it?
 
Originally posted by: PCboy
Originally posted by: Cerb
Originally posted by: GiLtY
If you are pressed for time (like you are taking a SAT test), just plug the answers in.

--GiLtY
Click to expand...
On such a test, you can bring calculators that can also make that extremely fast. Unfortunately teachers tend to like work 🙂

-Ernie, who knows he's got to take Calc and Calc II in a semester or two.
Click to expand...

can a ti-85 do it?
Click to expand...
Not sure. My TI-83p didn't come with an equation solver, so with my bored time in English and Chemistry classes, mastered BASIC for it, and made an (somewhat limited and quirky) equation solver. However, it was very simple to make a basic program for such problems, where you gave it variables, and an expression (string that gets converted when it does the math), or multiple expressions, and it tested values. Most of the time it was easier just to do that.
 
Originally posted by: Cerb
Originally posted by: PCboy
Originally posted by: Cerb
Originally posted by: GiLtY
If you are pressed for time (like you are taking a SAT test), just plug the answers in.

--GiLtY
Click to expand...
On such a test, you can bring calculators that can also make that extremely fast. Unfortunately teachers tend to like work 🙂

-Ernie, who knows he's got to take Calc and Calc II in a semester or two.
Click to expand...

can a ti-85 do it?
Click to expand...
Not sure. My TI-83p didn't come with an equation solver, so with my bored time in English and Chemistry classes, mastered BASIC for it, and made an (somewhat limited and quirky) equation solver. However, it was very simple to make a basic program for such problems, where you gave it variables, and an expression (string that gets converted when it does the math), or multiple expressions, and it tested values. Most of the time it was easier just to do that.
Click to expand...

there was a SOLVER function or something like that where you press the yellow 2nd button but it could only find one variable... most of the problems i had was equations with several variables with fractions and it was an ass..... i hated isolating variables and quadratic formulas.
 
Originally posted by: Woodchuck2000
You can't just plug the answers in and see which one works, as you have no values for Y. You'll have to solve it as Cerb described.
Click to expand...
Actually, while I can't make a proof for it (I haven't taken a real math class in around 3 years now--not counting trig, since that was memorization more than anything--so can't recall the various properties and such, and no longer have my notes), with those two equations, it's pretty obvious that x and y can be switched around, and as such, "x = ? and x= ??" works out as "(x= ? and y = ??) or (x = ?? and y = ?)".
x + y = 1
x^2 + y^2 = 25
In addition, order does not matter. Also, both are adding similar numbers (x^1 and y^1, then x^2 and y^2), so if x is this, y must be the that, or if x is that, y must be this. In either case, there are infinite solutions, so you need both equations to find a single one, though any integer and most squares should work for the side sides.

-Ernie, who has an intuitive understanding of these things, but simply has never been able to manage an A in a math class.
 
Originally posted by: PCboy
Originally posted by: Cerb
Originally posted by: PCboy
Originally posted by: Cerb
Originally posted by: GiLtY
If you are pressed for time (like you are taking a SAT test), just plug the answers in.

--GiLtY
Click to expand...
On such a test, you can bring calculators that can also make that extremely fast. Unfortunately teachers tend to like work 🙂

-Ernie, who knows he's got to take Calc and Calc II in a semester or two.
Click to expand...

can a ti-85 do it?
Click to expand...
Not sure. My TI-83p didn't come with an equation solver, so with my bored time in English and Chemistry classes, mastered BASIC for it, and made an (somewhat limited and quirky) equation solver. However, it was very simple to make a basic program for such problems, where you gave it variables, and an expression (string that gets converted when it does the math), or multiple expressions, and it tested values. Most of the time it was easier just to do that.
Click to expand...

there was a SOLVER function or something like that where you press the yellow 2nd button but it could only find one variable... most of the problems i had was equations with several variables with fractions and it was an ass..... i hated isolating variables and quadratic formulas.
Click to expand...
I didn't...then again, I made a quadratic equation solver that showed each step from filling in the quadratic equation values to getting the two final answers and checking them.
Also, with the str->expr() function somewhere in there, it was simple to solve for one variable and near automatically have it plugged in (make a program that just takes your expression, as a string, fills in the "solved for x" part, converts it to an expression, and gets one step closer to the answer...really great for tests).

Now I have the urge to make these things again, just to make sure I still have the knack 🙂
 
[1] - I had to stop winamp so I could remember the song . [-b +/- sqrt(b^2 - 4ac)] / 2a
Click to expand...
lmao! Da...da-da-da-da-da-da-da...all divided by two A.

I forget, was that sung to U of M's "Hail to the Victors" or "The Yellow and the Blue" fight song?

I was singing this for absolutely no apparent reason about a month ago. Damned math teacher. Taught me a nifty song I'll never forget...except I completely forgot how to do the math part. 😕

-Tim, who has no intuition about these things, still managed an A in his math classes, but promptly forgot everything over the summer break and started college as though he had never taken them to begin with. :disgust:
 
Originally posted by: tcsenter
[1] - I had to stop winamp so I could remember the song . [-b +/- sqrt(b^2 - 4ac)] / 2a
Click to expand...
lmao! Da...da-da-da-da-da-da-da...all divided by two A.

I forget, was that sung to U of M's "Hail to the Victors" or "The Yellow and the Blue" fight song?

I was singing this for absolutely no apparent reason about a month ago. Damned math teacher. Taught me a nifty song I'll never forget...except I completely forgot how to do the math part. 😕

-Tim, who has no intuition about these things, still managed an A in his math classes, but promptly forgot everything over the summer break and started college as though he had never taken them to begin with. :disgust:
Click to expand...
Yeah...something to do with how classes work. I Get It?, but struggle for a C, usually. On the other hand, I remember and can use it.
But, if I ever have to divide polynomials outside of a math class, I'll probably go crazy.

 
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