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Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 5 - Systems and MatricesProblem 16
Chapter 6, Problem 16

Graph each inequality. x < 3 + 2y

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Rewrite the inequality to isolate \( y \) on one side. Starting with \( x < 3 + 2y \), subtract 3 from both sides to get \( x - 3 < 2y \).
Divide both sides of the inequality by 2 to solve for \( y \): \( \frac{x - 3}{2} < y \). This can be rewritten as \( y > \frac{x - 3}{2} \).
Identify the boundary line for the inequality, which is \( y = \frac{x - 3}{2} \). Since the inequality is strict (\( > \)), the boundary line will be dashed on the graph.
Determine which side of the boundary line to shade. Pick a test point not on the line, such as \( (0,0) \), and substitute into the inequality \( y > \frac{x - 3}{2} \). If the test point satisfies the inequality, shade that side; otherwise, shade the opposite side.
Draw the dashed boundary line \( y = \frac{x - 3}{2} \) on the coordinate plane and shade the region above the line (if the test point satisfies the inequality) to represent all solutions to the inequality.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Inequalities in Two Variables

An inequality involving two variables, like x and y, represents a region in the coordinate plane where the inequality holds true. Instead of a single line, the solution is a shaded area that satisfies the inequality condition.
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Graphing Linear Inequalities

To graph a linear inequality, first rewrite it in a form that relates x and y, then graph the boundary line (using equality). Use a solid line if the inequality includes equality (≤ or ≥), or a dashed line if it does not (< or >).
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Testing Points to Determine Shading

After drawing the boundary line, select a test point not on the line (commonly (0,0)) to check if it satisfies the inequality. Shade the side of the line where the inequality holds true, representing all solutions.
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Determinants of 2×2 Matrices
Related Practice
Textbook Question

Solve each system by substitution.

3y = 5x + 6

x + y = 2

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components.

x2 - y = 0

x + y = 2

Textbook Question

Solve each problem using a system of equations. A company sells recordable CDs for \(0.80 each and play-only CDs for \)0.60 each. The company receives \$76.00 for an order of 100 CDs. However, the customer neglected to specify how many of each type to send. Determine the number of each type of CD that should be sent.

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Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x^2 - x - 15)/(x(x + 1)(x - 1))

Textbook Question

Find the values of the variables for which each statement is true, if possible.

[xyz]=[216]\(\left\)[ \(\begin{matrix}\) x & y & z \(\end{matrix}\) \(\right\)] = \(\left\)[ \(\begin{matrix}\) 21 & 6 \(\end{matrix}\) \(\right\)]

Textbook Question

Write the system of equations associated with each augmented matrix . Do not solve.

[321102422−1−2315]\(\left\)[ \(\begin{matrix}\) 3 & 2 & 1 & 1 \\ 0 & 2 & 4 & 22 \\ -1 & -2 & 3 & 15 \(\end{matrix}\) \(\right\)]

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