To solve this problem, we can simply substitute in the coordinate values for [tex]x[/tex] and [tex]y[/tex] in the equation:
[tex]2x - 9y = 38[/tex]
First ordered pair
[tex]2(7) - 9(5) \stackrel{?}{=} 38[/tex]
[tex]14 - 45 \stackrel{?}{=} 38[/tex]
[tex]-31 \neq 38[/tex]
The first ordered pair is not the answer.
Second ordered pair
[tex]2(4) - 9(-1) \stackrel{?}{=} 38[/tex]
[tex]8 + 9 \stackrel{?}{=} 38[/tex]
[tex]17 \neq 38[/tex]
The second ordered pair is not the answer.
Third ordered pair
[tex]2(3) - 9(-3) \stackrel{?}{=} 38[/tex]
[tex]6 + 27 \stackrel{?}{=} 38[/tex]
[tex]33 \neq 38[/tex]
The third ordered pair is not the answer.
Fourth ordered pair
[tex]2(1) - 9(-4) \stackrel{?}{=} 38[/tex]
[tex]2 + 36 \stackrel{?}{=} 38[/tex]
[tex]38 = 38[/tex]
The fourth ordered pair is the solution.
The solution is the fourth ordered pair.
