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}{x+3y=11x−5y=−13

Ch. 5 - Systems of Equations and Inequalities

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Blitzer 8th Edition

Ch. 5 - Systems of Equations and Inequalities

문제 1

6장, 문제 1

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

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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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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.

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.

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.

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 \(\end{cases}\){x+3y=11x−5y=−13