Q. 336 - Intermediate Algebra

Question

In the following exercises, without graphing determine the number of solutions and then classify the system of equations.

$\left\{\begin{array}{l}5x-4y=0\\ y=\frac{5}{4}x-5\end{array}\right.$

Step-by-Step Solution

Answer

The system of equations has no solutions that are parallel lines, inconsistent, and independent.  

Step 1. Given information.

The system of equations,

$\left\{\begin{array}{l}5x-4y=0\\ y=\frac{5}{4}x-5\end{array}\right.$

Step 2. Solving the first equation for y and finding the slope and y -intercept.

$$\begin{gathered} 5x-4y=0 \\ 4y=5x \\ x=\frac{5}{4}y \end{gathered}$$

Then the slope is $\frac{5}{4}$

And the $y$-intercept is $0$.

Step 3. Solving the second equation for y and finding the slope and y -intercept.

$y=\frac{5}{4}x-5$

Then the slope is $\frac{5}{4}$

And the $y$-intercept is $-5$.

Step 4. Required answer.

Here the slopes are the same and $y$-intercepts are different.

Hence the system of equations has no solutions that are parallel lines, inconsistent, and independent.