Determine whether an ordered pair solves a system of equations

An ordered pair solves a system of two linear equations when substituting its coordinates for the variables makes both equations true simultaneously; graphically, it represents the common point of the two lines. This reasoning distinguishes satisfying one equation from satisfying the system and supports interpreting solutions obtained by graphing, substitution, or elimination. The focus is on two-variable linear systems with numerical coordinates, not nonlinear systems, multiple variables, or parameterized edge cases.

Detailed Explanation: Determine whether an ordered pair solves a system of equations

To determine whether an ordered pair solves a system, substitute the $x$ -coordinate and $y$ -coordinate into both equations. The pair is a solution only if both equations are true.

Consider the system:

\begin{cases} y=2x-1\\ x+y=5 \end{cases}

Check whether $(2,3)$ is a solution.

Identify the coordinates: $x=2$ and $y=3$ .
Substitute into the first equation:

y=2x-1

3=2(2)-1

3=4-1

3=3

The first equation is true.

Substitute into the second equation:

x+y=5

2+3=5

5=5

The second equation is also true.

Since $(2,3)$ makes both equations true, $(2,3)$ is a solution to the system. Graphically, this means $(2,3)$ is the point where the two lines intersect.

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Verify a Solution to a Linear System - System to Substituted Equation

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Determine whether an ordered pair solves a system of equations

Detailed Explanation: Determine whether an ordered pair solves a system of equations

Learn by doing: Determine whether an ordered pair solves a system of equations

Practice with unlimited practice problems

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Verify a Solution to a Linear System - System to Substituted Equation