Q. 23 - Intermediate Algebra

Question

In the following exercises, solve the system of linear equations by graphing.

$\left\{\begin{array}{l}2x+y=6\\ -8x-4y=-24\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the system  $\left\{\begin{array}{l}2x+y=6\\ -8x-4y=-24\end{array}\right.$  has infinitely many solutions. It is found  by the graph as,

Step 1. Given information.

Consider the given system of linear equations.

$$\begin{gathered} 2x+y=6 \\ -8x-4y=-24 \end{gathered}$$

Step 2. Solve the first equation for y.

Find slope and y-intercept of the first equation.

$$\begin{gathered} 2x+y=6 \\ y=-2x+6 \end{gathered}$$

Here the slope m=$-2$ and the y-intercept is b =6.

Step 3. Solve the second equation for y .

Find slope and y-intercept of the second equation.

$$\begin{gathered} -8x-4y=-24 \\ -4y=8x-24 \\ y=(-2)x+6 \end{gathered}$$

Here the slope is m=$-2$ and, the y-intercept b= 6.

Step 4.Graph both the lines.

The graph of both equations on the same plane is drawn below,

• The lines are the same.
• Since every point on the line makes both equations true, there are infinity-ordered pairs that make both equations true.
• Therefore, there are infinitely many solutions to this system.