Q. 280 - Intermediate Algebra

Question

In the following exercise, determine whether each ordered pair is a solution to the system.

$\left\{\begin{array}{l}3x+y>5\\ 2x-y\le 10\end{array}\right.$

ⓐ $(3, -3)$

ⓑ $(7, 1)$

Step-by-Step Solution

Answer

Part (a). Ordered pair $\left(3,3\right)$ is the solution of the given system to inequalities.

Part (b). Ordered pair $(7,1)$ is not the solution to the given system of inequalities.

Part (a) Step 1. Substitute 3 , 3 in the given system of inequalities.

Substituting  $$\begin{gathered} x=3 \\ y=3 \end{gathered}$$ in the inequality

$3x+y>5$:

$$\begin{gathered} 3 x+y>5 \\ 3\left(3\right)-3>5 \\ 9-3>5 \\ 6>5 \end{gathered}$$

This is true.

Substituting $$\begin{gathered} x=3 \\ y=3 \end{gathered}$$ in the inequality

$2x-y\le 10$:

$$\begin{gathered} 2x-y\le 10 \\ 2\left(3\right)-(-3)\le 10 \\ 6+3\le 10 \\ 9\le 10 \end{gathered}$$

This is also true.

Thus, the ordered pair $\left(3,3\right)$ is the solution of the given in system of inequalities.

Part (b) step 1. Substitute 7 , 1 in the given system of inequalities.

Substituting $$\begin{gathered} x=7 \\ y=1 \end{gathered}$$ in the inequality

$3x+y>5$:

$$\begin{gathered} 3 x+y>5 \\ 3\left(7\right)+1>5 \\ 21+1>5 \\ 22>5 \end{gathered}$$

This is true.

Substituting $$\begin{gathered} x=7 \\ y=1 \end{gathered}$$ in the inequality

$2x-y\le 10$:

$\begin{array}{r}2x-y\le 10\\ 2\left(7\right)-1\le 10\\ 14-1\le 10\\ 13\le 10\end{array}$

This is not true.

Thus, $\left(7,1\right)$ is not a solution of the given system of equation.