Q 4 - Intermediate Algebra

Question

In the following exercises, determine if the following points are solutions to the given system of equations.

$\left\{\begin{array}{l}2x+3y=6\\ y=\frac{2}{3}x+2\end{array}\right.$

a.$(-6,2)$

b.$(-3,4)$

Step-by-Step Solution

Answer

For (a), the ordered pair, $(-6,2)$ is not a solution of the system of linear equations.

For (b), the ordered pair $(-3,4)$ is not a solution of the system of linear equations.

Part (a) Step 1: Given information

Given the system of equations  $\left\{\begin{array}{l}2x+3y=6\\ y=\frac{2}{3}x+2\end{array}\right.$

and ordered pair $(-6,2)$

Part (a)Step 2: Checking the values

Substituting the values, we get 

$$\begin{gathered} \begin{array}{r}2x+3y=6\\ 2(-6)+3\left(2\right)=6\end{array} \\ -12+6=6 \\ -6=6 \end{gathered}$$

Not correct 

Part (a) Step 3: Substitute for another equation

Substituting the values, we get 

$$\begin{gathered} y=\frac{2}{3}x+2 \\ 2=\frac{2}{3}(-6)+2 \\ 2=-4+2 \\ 2=-2 \end{gathered}$$

Not correct

Part (b) Step 1: Given information

Given the system of equations $\left\{\begin{array}{l}2x+3y=6\\ y=\frac{2}{3}x+2\end{array}\right.$ and ordered pair $(-3,4)$

Part (b) Step 2: Checking the value

Substituting the value, we get

$$\begin{gathered} 2(-3)+3\left(4\right)=6 \\ -6+12=6 \\ 6=6 \end{gathered}$$

It is true

Part (b) Step 3: Checking the value

Substituting, we get

$$\begin{gathered} 2=\frac{2}{3}(-6)+2 \\ 2=-4+2 \\ 2=-2 \end{gathered}$$

This is not true