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All courses Algebra I · A-REI.10 6 of 76
Understand that a two-variable equation's graph is the set of all ordered-pair solutions.

Test whether an ordered pair satisfies an equation

Problem
Test \((4,14)\) in \(y=3x+2\).
Your answer
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Hint

Substitute x = 4 and y = 14 into the equation y = 3x + 2.

An ordered pair satisfies an equation if replacing x and y with its coordinates makes both sides equal.

Solution walkthrough

01

Map coordinate order to variables

\[(4,14)~\text{means}~x=4~\text{and}~y=14\]

Ordered pairs use (x,y) order. Both coordinates must be substituted into y = 3x + 2.

02

Evaluate the equation's right side

\[3x+2=3(4)+2=12+2=14\]

Use the given x-coordinate 4, multiply first, and add 2. The equation predicts output 14.

03

Compare predicted and given output

\[\text{left}~y=14;~\text{right}~3(4)+2=14;~14=14\]

The predicted y-value equals the point's supplied y-coordinate, so substitution makes a true statement.

04

State the complete satisfaction record

\[\text{left}~=~14;~\text{right}~=~14;~\text{equal}~=~\text{yes};~\text{satisfies}~=~\text{yes}\]

Both evaluated sides and the resulting point judgment exactly match choice A.

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Another way

  1. Compute the output for x = 4 first: y = 14. Since that creates exactly the listed pair (4,14), the pair satisfies the equation.

!

Common mistake

Do not substitute only x and stop. A point is a solution only when the computed output matches its given y-coordinate.

Solution walkthrough video