Question

question 4 of 10, step 1 of 1
use the method of substitution 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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$$\begin{cases} -y = -38 \\\\ 5x + y = -42 \\end{cases}$$

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

Explanation:

Step1: Solve for $y$ from first equation

From $-y = -38$, multiply both sides by $-1$:
$y = 38$

Step2: Substitute $y$ into second equation

Substitute $y=38$ into $5x + y = -42$:
$5x + 38 = -42$

Step3: Isolate $5x$ term

Subtract 38 from both sides:
$5x = -42 - 38$
$5x = -80$

Step4: Solve for $x$

Divide both sides by 5:
$x = \frac{-80}{5} = -16$

Answer:

Only One Solution
$x=-16$, $y=38$