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All courses Math I · A-REI.10 6 of 59
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. Enter the substituted left value, right value, equality yes/no, and satisfies yes/no.
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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

Substitute the x-value

\[y~=~3(4)~+~2\]

Replace x with 4 in the equation y = 3x + 2.

02

Substitute the y-value

\[14~=~3(4)~+~2\]

The ordered pair gives y = 14, so replace y with 14 as well.

03

Simplify the right side

\[\begin{aligned} 14~=~12~+~2 \\ 14~=~14 \end{aligned}\]

Compute 3 times 4, then add 2. The two sides match.

04

State the conclusion

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

Because substitution makes a true statement, the ordered pair is a solution.

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Another way

  1. You can compute the right side first: 3(4) + 2 = 14, which matches the y-value in the ordered pair.

!

Common mistake

A common mistake is to substitute only x and forget to compare the result to the given y-value. Both coordinates must be checked.