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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

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

 

3. 

 

 Jul 24, 2020
 #2
avatar+359 
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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
avatar+186 
+1

Thank you! I was able to solve it after this.

Caffeine  Jul 26, 2020
 #4
avatar+359 
+5

no problem!!!

iamhappy  Jul 27, 2020

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