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Determining Whether an Ordered Pair Is a Solution to a System of Equations · Physics Playground

Exercises Systems of equations

Example 1 from Algebra and Trigonometry, 11.1 Systems of Linear Equations: Two Variables

Determining Whether an Ordered Pair Is a Solution to a System of Equations

Determine whether the ordered pair $(5, 1)$ is a solution to the given system of equations.

\begin{array}{l} x + 3 y = 8 \\ 2 x - 9 = y \end{array}

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Substitute the ordered pair $(5, 1)$ into both equations.
$\begin{array}{l} (5) + 3 (1) = 8 \\ 8 = 8 & True \\ 2 (5) - 9 = (1) \\ 1=1 & True \end{array}$
The ordered pair $(5, 1)$ satisfies both equations, so it is the solution to the system.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Determine whether the ordered pair $(8, 5)$ is a solution to the following system.

\begin{matrix} 5 x −4 y = 20 \\ 2 x + 1 = 3 y \end{matrix}

How did it go?

PreviousGraphing Systems of Linear Inequalities: example 5.58 Next Solving a System of Equations in Two Variables by Graphing

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 11.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.