Q. 19 - Intermediate Algebra

Question

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

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

Step-by-Step Solution

Answer

The solution of the system $\left\{\begin{array}{l}4x-3y=8\\ 8x-6y=14\end{array}\right.$ has no solution. It is found  by a graph as,

Step 1. Given information.

Consider the given equations,

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

Step 2. Solve the first equation for y.

Find the slope and y-intercept of the first equation.

$\begin{array}{rcl}4x-3y& =& 8\\ -3y& =& -4x+8\\ y& =& \frac{4}{3}x-\frac{8}{3}\end{array}$

Here the slope is $m=\frac{4}{3}$ and, the y-intercept is $b=-\frac{8}{3}$.

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

Find the slope and y-intercept of the second equation.

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

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 parallel.
• Since, no point in both lines, there is no ordered pair that makes both equations true.
• Therefore, no solution to this system.