Question

give the solution of the system.
\

$$\begin{cases} 3x - y = 14 \\\\ -6x + 2y = -28 \\end{cases}$$

when solving, you obtain 0 = 0.
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\bigcirc a. the solution is \square. (type an ordered pair, using integers or decimals.)
\bigcirc b. there is an infinite number of solutions.
\bigcirc c. there is no solution.

Explanation:

Step1: Analyze the system of equations

The system is \(

$$\begin{cases}3x - y = 14\\-6x + 2y = -28\end{cases}$$

\). Notice that the second equation can be obtained by multiplying the first equation by \(-2\). Let's check: Multiply \(3x - y = 14\) by \(-2\), we get \(-6x + 2y = -28\), which is exactly the second equation. So the two equations are dependent (they represent the same line).

Step2: Determine the number of solutions

When we solve a system of linear equations and get a statement like \(0 = 0\) (a true statement), it means the two equations are equivalent, and there are infinitely many solutions because every point on the line represented by one equation is also on the line represented by the other equation.

Answer:

B. There is an infinite number of solutions.