Question

solve the following system of linear equations by addition. indicate whether the given system of linear equations is consistent, inconsistent, or dependent. if the system is consistent, find the solution.
\\(\

$$\begin{cases}1.5x - 1.5y = 10.5\\4.5x - 4.5y = 31.5\\end{cases}$$

\\)
answer 5 points
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consistent ( )
inconsistent
dependent

Explanation:

Step1: Multiply the second - equation by 3

Multiply the equation \(1.5x−1.5y = 10.5\) by 3. We get \(4.5x−4.5y=31.5\), which is the same as the first equation \(4.5x - 4.5y=31.5\).

Step2: Determine the nature of the system

Since the two equations are essentially the same, the system is dependent.

Answer:

Dependent