Create a practice test about determining if an ordered pair is a solution of a system of equations in two variables.
Understand the Problem
The question is asking for the creation of a practice test focused on determining whether an ordered pair is a solution to a system of equations in two variables. This involves checking if the pair satisfies both equations in the system.
Answer
The ordered pair $(1, 5)$ is not a solution to the system of equations.
Answer for screen readers
The ordered pair $(1, 5)$ is not a solution to the system of equations.
Steps to Solve

Identify the system of equations Determine the two equations that need to be checked against the ordered pair. For example, let’s consider the system: $$ y = 2x + 3 $$ $$ y = x + 1 $$

Substitute the ordered pair into one equation Take the ordered pair, say $(x, y) = (1, 5)$, and substitute it into one of the equations. Let's use the first equation: $$ y = 2x + 3 $$ Substituting $x = 1$ gives: $$ 5 = 2(1) + 3 $$

Simplify and check Now simplify the right side: $$ 5 = 2 + 3 \implies 5 = 5 $$ This is true, so the ordered pair satisfies the first equation.

Substitute the ordered pair into the second equation Now we check the second equation with the same ordered pair $(1, 5)$: $$ y = x + 1 $$ Substituting $x = 1$ gives: $$ 5 = (1) + 1 $$

Simplify and check Now simplify the right side: $$ 5 = 1 + 1 \implies 5 = 0 $$ This is false, meaning the ordered pair does not satisfy the second equation.

Conclusion Since the ordered pair satisfies the first equation but not the second, it is not a solution to the system of equations.
The ordered pair $(1, 5)$ is not a solution to the system of equations.
More Information
When determining if an ordered pair is a solution to a system of equations, it must satisfy all equations in the system. If it does not satisfy even one equation, it is not a solution.
Tips
 Forgetting to substitute into both equations can lead to incorrect conclusions about the ordered pair.
 Miscalculating during the substitution or simplification steps can yield false results.
 Not remembering that both equations must be satisfied for the ordered pair to be considered a solution.
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