Question

question 7 of 10, step 1 of 1
use the method of elimination to solve the following system of equations. if the system is dependent, express the solution set in terms of one of the variables. leave all fractional answers in fraction form.
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$$\begin{cases} -3x - 4y = 1 \\\\ 15x + 20y = -6 \\end{cases}$$

answer
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\bigcirc only one solution
\bigcirc inconsistent system
\bigcirc dependent system

Explanation:

Step1: Eliminate $x$ variable

Multiply first equation by 5:
$$5(-3x - 4y) = 5(1) \implies -15x - 20y = 5$$

Step2: Add to second equation

Add new equation to $15x + 20y = -6$:
$$(-15x - 20y) + (15x + 20y) = 5 + (-6)$$
$$0 = -1$$

Step3: Analyze the result

The equation $0=-1$ is a false statement, meaning there are no solutions to the system, so it is inconsistent.

Answer:

Inconsistent System