An ordered pair is a solution to a linear system precisely when its two coordinates make both linear equations true simultaneously; it represents a common point of the equations’ graphs, not merely a point on one line. Determining this involves substituting the coordinates into each equation and evaluating equality, including cases with integer, decimal, or fractional values, while recognizing that a system’s solution set may contain one point, no points, or infinitely many points.
An ordered pair solves a system when it makes both equations true at the same time. To check, substitute the -coordinate for and the -coordinate for in each equation.
Example: Determine whether solves the system
Step 1: Check the first equation.
Substitute and :
The first equation is true.
Step 2: Check the second equation.
The second equation is also true.
Because makes both equations true, it is a solution to the system. It represents the point where the two lines intersect.
If an ordered pair makes even one equation false, it is not a solution to the system.
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