Q. 18 - Intermediate Algebra

Question

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

$\left\{\begin{array}{l}3x+5y=10\\ y=-\frac{3}{5}x+1\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the system $\left\{\begin{array}{l}3x+5y=10\\ y=-\frac{3}{5}x+1\end{array}\right.$ has no solution. It is found by a graph as,

Step 1. Given information.

Given the system of linear equations,

$\begin{array}{rcl}3x+5y& =& 10\\ y& =& -\frac{3}{5}x+1\end{array}$

Step 2. Solve the first equation for y.

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

$\begin{array}{rcl}3x+5y& =& 10\\ 5y& =& -3x+10\\ y& =& -\frac{3}{5}x+2\end{array}$

Here the slope m= -$\frac{3}{5}$and,the y-intercept b=2.

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.

$y=-\frac{3}{5}x+1$

Here the slope is m=$-\frac{3}{5}$and, the y-intercept is b=1.

Step 4. Graph both the lines.

The graph of both lines on one 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.