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If an ordered pair is a solution to a system of linear equations, then algebraically it returns the same values when substituted appropriately into the x and y variables in each equation. For a very basic example:

(0,0) satisfies the linear system of equations given by y=x and y=-2x

By substituting in x=0 into both equations, the following is obtained:

y=(0) and y=-2(0)=0

x=0 returns y=0 for both equations, which satisfies the ordered pair (0,0).

This means that if an ordered pair is a solution to a system of equations, the x of that ordered pair returns the same y for all equations in the system.

Graphically, this means that all equations in the system intersect at that point. This makes sense because an x value returns the same y value at that ordered pair, meaning all equations would have the same value at the x-coordinate of the ordered pair. The ordered pair specifies an intersection point of the equations.

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