+284 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!!!
+569 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. :)
