Q. 24 - Intermediate Algebra

Question

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

$\left\{\begin{array}{l}5x+2y=7\\ -10x-4y=-14\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the system $\left\{\begin{array}{l}5x+2y=7\\ -10x-4y=-14\end{array}\right.$has infinity many solutions.   It is found  by a graph as,

Step 1. Given information.

Consider the given system of linear equations,

$$\begin{gathered} 5x+2y=7 \\ -10x-4y=-14 \end{gathered}$$

Step 2. Solve the first equation for y.

Find slope and y-intercept.

$$\begin{gathered} 5x+2y=7 \\ 2y=-5x+7 \\ y=(-\frac{5}{2})x+\frac{7}{2} \end{gathered}$$

Here the slope is m=$-\frac{5}{2}$ and the y-intercept is b=$\frac{7}{2}$.

Step 3. Solve the second equation for y.

Find the slope and y-intercept. 

$$\begin{gathered} -10x-4y=-14 \\ -4y=10x-14 \\ y=-\frac{5}{2}x+\frac{7}{2} \end{gathered}$$

Here the slope is m=$-\frac{5}{2}$and, the y-intercept is b=$\frac{7}{2}$.

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 infinity many solutions to this system.