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Math Topics

Intermediate Algebra

Systems of Equations

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1
Solving Linear Systems

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Systems of Linear Equations in Three Variables

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Matrix Solutions to Linear Systems

Give the dimensions of the following matrices.

\(\left[\begin{array}{cc} -2 & 1\\ 5 & 3 \end{array}\right]\)

\(\left[\begin{array}{cc} 1 & 0\\ 4 & -2\\ -3 & 7 \end{array}\right]\)

\(\left[\begin{array}{cc} 5\\ -2\\ 1 \end{array}\right]\)

\(\left[\begin{array}{cc} 4 & -2 \end{array}\right]\)

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Determinants and Cramerâ€™s Rule

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5
Applications of Systems of Equations

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 \(F\).

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6
System of Linear Inequalities and Applications

A basketball arena charges \(\$20\) for certain seats and \(\$15\) for others. They want to make more than \(\$18,000\) and reserve at least \(500\) \(\$15\) seats. Find the system of inequalities and sketch the graph. If \(620\) tickets are sold for \(\$15\), at least how many are sold for \(\$20\)?

Make-A-Sale is a new company designed to assist clients selling household items over the internet. Start-up costs for the company are \(\$40,000\), and they expect variable costs to be \(\$6.00\) for each item sold. They plan to charge \(\$14.00\) per item.

Find the total cost, revenue, and profit for selling \(x\) items.

If they sell \(3,000\) items, find their cost, revenue, and profit.

If they sell \(12,000\) items, find their cost, revenue, and profit.

Find the break-even point (when revenue equals cost), include a graph of the inequalities \(R(x)\leq C(x)\) and \(R(x)\geq C(x)\) to show intervals of profit and loss.