Q. 22 - Intermediate Algebra

Question

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

$\left\{\begin{array}{l}4x=3y+7\\ 8x-6y=14\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the system  $\left\{\begin{array}{l}4x=3y+7\\ 8x-6y=14\end{array}\right.$    has infinity many solutions.It is found  by graph as,

Step 1. Given information.

Consider the given system of linear equations,

$$\begin{gathered} 4x=3y+7 \\ 8x-6y=14 \end{gathered}$$

Step 2. Solve the first equation for y , and find slope and y -intercept.

Find slope and y-intercept of the first equation.

$\begin{array}{rcl}4x& =& 3y+7\\ 4x-7& =& 3y\\ \left(\frac{4}{3}\right)x-\frac{7}{3}& =& y\end{array}$

Here the slope is m=$\frac{4}{3}$and, the y-intercept b=$-\frac{7}{3}$.

Step 3.Solve the second equation for y,and find slope and y-intercept.

Find slope and y-intercept of the second equation.

$$\begin{gathered} 8x-6y=14 \\ -6y=-8x+14 \\ y=\frac{4}{3}x-\frac{7}{3} \end{gathered}$$

Here the slope is m=$\frac{4}{3}$ and, the y-intercept is b=$-\frac{7}{3}$.

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 equation true.
• Therefore,there are infinity many solotions to this system.