Determine whether each ordered pair is a solution to the following system:

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

1. \((-2,5)\)

2. \((10,-7)\)

Solve the following system by graphing:

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

Solve the following system by graphing:

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

Mini Lecture
Solve each system.

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

2. \(\begin{aligned}[t] 3 x -2 y &= 6 \\ x-y &= 1 \end{aligned}\)

3. \(\begin{aligned}[t] x + y &= 2 \\ x &= -3 \end{aligned}\)

Common Mistake This is a mistake in using notation incorrectly.

Solve the system.

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

Solve the system.

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

Mini Lecture
Solve each system.

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

2. \(\begin{aligned}[t] 3 x - y &= 4 \\ 2x+2y &= 24 \end{aligned}\)

3. \(\begin{aligned}[t] 2x + 9y &= 2 \\ 5x+3y &= -8 \end{aligned}\)

Solve the following system by the substitution method:

\[\begin{aligned} 2x-3y&= 12\\ x&= 2y+7\end{aligned}\]

There are two cell phone contract rates, at how many minutes will the two contracts cost the same?

Mini Lecture
Solve each system.

1. \(\begin{aligned}[t] x + y &= 11 \\ y &= 1x-1 \end{aligned}\)

2. \(\begin{aligned}[t] 2 x + y &= 1 \\ x-5y &= 17 \end{aligned}\)

3. \(\begin{aligned}[t] 7x - 6y &= -1 \\ x &= 2y-1 \end{aligned}\)

SAT Exam: Multiple Choice Question

Mini Lecture

1. Two positive numbers have a difference of \(5\). The larger is one more than twice the smaller. Find the two numbers.

2. A woman invests \(4\) times as much money at \(5\%\) than she does at \(6\%\). The total interest for the year is \(\$520\). How much is invested at each rate?

3. Tom has \(21\) coins totaling \(\$3.45\). The coins are dimes and quarters. How many of each type does he have?

4. How many liters of \(50\%\) alcohol solution and \(20\%\) alcohol solution must be mixed to obtain \(18\) liters of \(30\%\) solution?