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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 1
Chapter 6, Problem 1

Match each system of inequalities with the correct graph from choices A–D. x ≥ 5 y ≤ -3

Verified step by step guidance
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Step 1: Understand the inequalities given: \(x \geq 5\) means the solution includes all points to the right of and on the vertical line \(x=5\). \(y \leq -3\) means the solution includes all points below and on the horizontal line \(y=-3\).
Step 2: Identify the boundary lines on the graphs. The vertical line at \(x=5\) should be solid (because of the \(\geq\) sign) and the shading should be to the right of this line.
Step 3: The horizontal line at \(y=-3\) should also be solid (because of the \(\leq\) sign) and the shading should be below this line.
Step 4: Look for the graph where the shaded region is the intersection of the two conditions: to the right of \(x=5\) and below \(y=-3\). This means the shaded area should be in the lower right quadrant formed by these two lines.
Step 5: Match this description to the correct graph choice. The graph that shows shading to the right of \(x=5\) and below \(y=-3\) with solid boundary lines is the correct match.

Key Concepts

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

Graphing Linear Inequalities

Graphing linear inequalities involves shading the region of the coordinate plane that satisfies the inequality. For example, x ≥ 5 means shading all points to the right of the vertical line x = 5, including the line itself if it is solid.
Recommended video:
06:07
Linear Inequalities

Interpreting Boundary Lines

The boundary line of an inequality is drawn as solid if the inequality includes equality (≥ or ≤) and dashed if it does not (> or <). This line divides the plane into two halves, one of which satisfies the inequality.
Recommended video:
06:49
The Slope of a Line

Combining Systems of Inequalities

When dealing with a system of inequalities, the solution is the intersection of the shaded regions for each inequality. For x ≥ 5 and y ≤ -3, the solution is where the shaded region to the right of x=5 overlaps with the shaded region below y=-3.
Recommended video:
6:19
Systems of Inequalities
Related Practice
Textbook Question

Answer each question. By what expression should we multiply each side of 5/((3x(2x + 1)) = A/(3x) + B/(2x + 1) so that there are no fractions in the equation?

Textbook Question

What is the value of ∣40−20∣\(\left\)| \(\begin{matrix}\) 4 & 0 \\ -2 & 0 \(\end{matrix}\) \(\right\)| ?

2
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Textbook Question

How many rows and how many columns does this matrix have? What is its dimension?

[−2580113−69]\(\left\)[ \(\begin{matrix}\) -2 & 5 & 8 & 0 \\ 1 & 13 & -6 & 9 \(\end{matrix}\) \(\right\)]

7
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Textbook Question

Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence. The following nonlinear system has two solutions, one of which is (3,____).

x + y = 7

x2 + y2 = 25

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Textbook Question

Answer each question. What is the product of [64−18]\(\left\)[ \(\begin{matrix}\) 6 & 4 \\ -1 & 8 \(\end{matrix}\) \(\right\)] and I2 (in either order)?

Textbook Question

Fill in the blank(s) to correctly complete each sentence. For the following statement to be true, the value of x must be ____, and the value of y must be ____.

[3−651]=[x+1−65y+1]\(\left\)[ \(\begin{matrix}\) 3 & -6 \\ 5 & 1 \(\end{matrix}\) \(\right\)] = \(\left\)[ \(\begin{matrix}\) x + 1 & -6 \\ 5 & y + 1 \(\end{matrix}\) \(\right\)]