Q. 20 - Intermediate Algebra

Question

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

$\left\{\begin{array}{l}x+3y=4\\ -2x-6y=3\end{array}\right.$

Step-by-Step Solution

Answer

The system of equations $\left\{\begin{array}{l}x+3y=4\\ -2x-6y=3\end{array}\right.$has no solution and it can be seen in the graph as,

Step 1. Given information.

Consider the given System of linear equations,

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

Step 2. Solve the first equation for y.

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

$\begin{array}{rcl}x+3y& =& 4\\ 3y& =& -x+4\\ y& =& (-\frac{1}{3})x+\frac{4}{3}\end{array}$

Here the slope is m=$-\frac{1}{3}$and, the y-intercept is b=$\frac{4}{3}$.

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.

$\begin{array}{rcl}-2x-6y& =& 3\\ -6y& =& 2x+3\\ y& =& (-\frac{1}{3})x-\frac{1}{2}\end{array}$

Here the slope is m=$-\frac{1}{3}$ and, the y-intercept is b= -1/2.

Step 4. Graph both the lines.

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

Image Caption

• 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.