Question

solve the system by the method of your choice.
$5x = y - 4$
$5x - y = 2$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}. (type an ordered pair.)
b. there are infinitely many solutions.
c. there is no solution.

Explanation:

Step1: Rearrange first equation

$5x - y = -4$

Step2: Compare to second equation

Second equation: $5x - y = 2$

Step3: Analyze consistency

We have

$$\begin{cases}5x - y = -4 \\ 5x - y = 2\end{cases}$$

. The left sides are identical, but the right sides $-4
eq 2$, so the system is inconsistent.

Answer:

C. There is no solution.