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# Algebra Questions

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Hi, could someone help me with these questions?

1. Find the ordered pair (s, t) that satisfies the system (s/2)+5t=3  3t-6s=9

2. For a certain value of k, the system

\begin{align*} 3a + 4b &= 7,\\ 6a + 4b &= k- 4b \end{align*}

has infinitely many solutions (a,b) What is k?

3. Real numbers x and y satisfy

\begin{align*} x + xy^2 &= 250y, \\ x - xy^2 &= -240y. \end{align*}
What are the possible values of x?

Thank you so much!!!

Jul 24, 2020

#1
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2. Using the determinant and Cramer's Ruler, we get that k = 28.

3. Jul 24, 2020
#2
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Great job guest with two and three, I give a shot at number one. :)

So I am assuming that in LaTeX, $$\frac{s}{2}+5t=3, 3t-6s=9$$ this is the system,

We can do substituiton or elimination, but I will do substitution.

Isolate s for The first equation to get $$s=6-10t$$,

Substitute $$6-10t$$ for s into the second equation to get $$\begin{bmatrix}3t-6\left(6-10t\right)=9\end{bmatrix}$$,

Simplify into $$63t-36=9$$,

And from here, I think that Caffeine should be able to do it him/herself. :)

Jul 24, 2020
#3
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Thank you! I was able to solve it after this.

Caffeine  Jul 26, 2020
#4
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no problem!!!

iamhappy  Jul 27, 2020