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Ch. 5 - Systems of Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 5 - Systems of Equations and InequalitiesProblem 1
Chapter 6, Problem 1

Determine whether the given ordered pair is a solution of the system. (2,3)(2, 3)
{x+3y=11x−5y=−13\(\begin{cases}\)x + 3y = 11 \(\x\) - 5y = -13\(\end{cases}\)

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1
Identify the ordered pair given, which is (2, 3). This means x = 2 and y = 3.
Substitute x = 2 and y = 3 into the first equation: \(x + 3y = 11\). This becomes \(2 + 3(3)\).
Simplify the left side of the first equation after substitution: calculate \(2 + 9\).
Check if the simplified left side equals the right side of the first equation, which is 11.
Repeat the substitution process for the second equation \(x - 5y = -13\) by substituting x = 2 and y = 3, then simplify and check if both sides are equal.

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Key Concepts

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

Systems of Linear Equations

A system of linear equations consists of two or more linear equations with the same set of variables. The solution to the system is the set of values for the variables that satisfy all equations simultaneously. Understanding how to interpret and work with these systems is essential for solving or verifying solutions.
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Ordered Pair as a Solution

An ordered pair (x, y) represents a potential solution to a system of equations. To verify if it is a solution, substitute the values of x and y into each equation. If both equations hold true, the ordered pair is a solution to the system.
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Substitution Method for Verification

The substitution method involves plugging the values of the ordered pair into each equation to check for equality. This direct substitution helps determine if the pair satisfies both equations, confirming whether it is a valid solution to the system.
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Related Practice
Textbook Question

Solve each system by the substitution method.

{x+y=2y=x2−4\(\begin{cases}\)x + y = 2 \(\y\) = x^2 - 4\(\end{cases}\)

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Textbook Question

Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants.(11x - 10)/(x − 2) (x + 1)

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Textbook Question

Determine if the given ordered triple is a solution of the system. (2,−1,3)(2,−1, 3)

{x+y+z=4x−2y−z=12x−y−2z=−1\(\begin{cases}\)x + y + z = 4 \(\x\) - 2y - z = 1 \\2x - y - 2z = -1\(\end{cases}\)