Mini Lecture
Solve:

1. \[\begin{aligned} 3x-5y &= -2\\ 2x-3y &= 1\end{aligned}\]

2. \[\begin{aligned} 4x-3y &= 2\\ 8x-6y &= 4\end{aligned}\]

3. \[\begin{aligned} \dfrac{1}{2}x-\dfrac{1}{3}y &= 2\\ \dfrac{1}{4}x+\dfrac{2}{3}y &= 6\end{aligned}\]

4. \[\begin{aligned} 2x-3y &= 2\\ y &= 3x-5\end{aligned}\]

Mini Lecture
Solve:

1. \[\begin{aligned} 2x+y-z &= 3\\ 3x+4y+z &= 6\\ 2x-3y+z &= 1\end{aligned}\]

2. \[\begin{aligned} x+3y &= 5\\ 6y+z &= 12\\ x-2z &= -10\end{aligned}\]

Mini Lecture
Evaluate.

1. \(\begin{vmatrix} 3&5\\ -2&7 \end{vmatrix}\)

2. \(\begin{vmatrix} x^2&2\\ x&1\end{vmatrix}\)

3. \(\begin{vmatrix} 1&3&-2\\ 2&0&1\\ 4&-1&1\end{vmatrix}\)

Mini Lecture
Solve:

1. \[\begin{aligned} 2x-3y&=4\\ 4x+5y&=3\end{aligned}\]

2. \[\begin{aligned} x+y&=-1\\ 2x-z&=3\\ y+2z&=-1\end{aligned}\]

Mini Lecture
Set up to solve by matrices:

1. \[\begin{aligned} x+y &= 5\\ 3x-y &= 3\end{aligned}\]

2. \[\begin{aligned} 2x-y &= 4\\ x+3y &= 9\end{aligned}\]

3. \[\begin{aligned} 2x-8y &= 6\\ 3x-8y &= 13\end{aligned}\]

Mini Lecture
Set up to solve by matrices:

1. \[\begin{aligned} x+y+z &= 4\\ x-y+2z &= 5\\ x-y-z &= 5\end{aligned}\]

2. \[\begin{aligned} x+2y &= 3\\ y+z &= 3\\ 4x-z &= 2\end{aligned}\]

If water at room temperature is \(77^{\circ}F\) or \(25^{\circ}C\). And the water boils at \(212^{\circ}F\) or \(100^{\circ}C\). Assume the relationship between the two scales is linear, find the formula that gives the Celsius temperature \(C\) in terms of Fahrenheit temperature \(F\).

Mini Lecture
Graph.

1. \(2x-3<6\)

2. \(y\geq x-5\)

3. \(y<2\)

Write the first five terms of the sequence with the following general term: \[a_n=3n-5\]

Write the first five terms of the sequence with the following general term: \[a_1=3,\, a_n=a_{n-1}+4,\, n>1\]

Write the first five terms of the sequence with the following general term: \[a_n=n^2+1\]

Write the first five terms of the sequence with the following general term: \[a_n=2n^3\]

Write the first five terms of the sequence with the following general term: \[a_n=\frac{n+1}{n^2}\]

Write the first five terms of the sequence with the following general term: \[a_1=4,\, a_n=-2a_{n-1},\, n>1\]

Give the general term of this sequence: \[6, 10, 14, 18, \ldots\]

Give the general term for this sequence: \[1, 2, 4, 8, \ldots\]

Give the general term for this sequence: \[\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \ldots\]

Give the general term for this sequence: \[-3, 9, -27, 81, \ldots\]

Expand and simplify each of the following:

1. \(\displaystyle\sum_{i=1}^5 (5i+3)\)

2. \(\displaystyle\sum_{i=3}^5 (2^i-1)\)

3. \(\displaystyle\sum_{i=2}^6 \left(i^2+2i\right)\)

Find the first term of an arithmetic progression if \(a_5=11\) and \(a_9=19\).

Find the second term of a geometric progression if \(a_3=18\) and \(a_5=162\).

Find the sum of the first \(10\) terms of this arithmetic progression: \[5, 11, 17, \ldots\]

Find the sum of the first \(10\) terms of this arithmetic progression: \[25, 20, 15, \ldots\]

Write a formula for the sum of the first \(50\) terms of this geometric progression: \[3, 6, 12, \ldots\]

Find the sum of \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}+\ldots\)

Use the binomial formula to expand: \[(x-3)^4\]

Use the binomial formula to expand: \[(2x-1)^5\]

Find the first \(3\) terms in the expansion of \[(x-1)^{20}\]

Find the sixth term in: \[(2x-3y)^8\]