In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (2, 3) x + 3y = 11 x - 5y = - 13

Verified step by step guidance

1. Step 1: Identify the ordered pair (2, 3) as the values for x and y respectively, where x = 2 and y = 3.
2. Step 2: Substitute x = 2 and y = 3 into the first equation $x+3y=11$. This gives $2\; +\; 3(3)\; =\; ?$.
3. Step 3: Simplify the left side of the first equation: $2\; +\; 9\; =\; 11$. Check if this equals the right side, which is 11.
4. Step 4: Substitute x = 2 and y = 3 into the second equation $x-5y=\; -13$. This gives $2\; -\; 5(3)\; =\; ?$.
5. Step 5: Simplify the left side of the second equation: $2\; -\; 15\; =\; -13$. Check if this equals the right side, which is -13.

Key Concepts

Systems of Linear Equations

A system of linear equations consists of two or more linear equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously. Understanding how to interpret and work with these systems is essential for solving problems involving multiple constraints.

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; otherwise, it is not.

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 the system, making it a straightforward approach to verify solutions without solving the system from scratch.