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Exercises Systems of equations

Example 5.51 from Elementary Algebra, 5.6 Graphing Systems of Linear Inequalities

Graphing Systems of Linear Inequalities: example 5.51

Determine whether the ordered pair is a solution to the system. ${\begin{matrix} x + 4 y \geq 10 \\ 3 x - 2 y < 12 \end{matrix}$

ⓐ (−2, 4) ⓑ (3,1)

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.

1
Solution
1. ⓐ Is the ordered pair (−2, 4) a solution?
The ordered pair (−2, 4) made both inequalities true. Therefore (−2, 4) is a solution to this system.
1. ⓑ Is the ordered pair (3,1) a solution?
The ordered pair (3,1) made one inequality true, but the other one false. Therefore (3,1) is not a solution to this 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 is a solution to the system.
${\begin{matrix} x - 5 y > 10 \\ 2 x + 3 y > −2 \end{matrix}$

ⓐ $(3, −1)$ ⓑ $(6, −3)$

How did it go?

PreviousSolve Mixture Applications with Systems of Equations: example 5.50 Next Graphing Systems of Linear Inequalities: example 5.52

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 5.6, 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.