Question

give the solution of the system. if the system has no solution or an infinite number of solutions, say so. if the \\(\

$$\begin{cases} 3x + 2y = 3 \\\\ x = y + 1 \\end{cases}$$

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

Explanation:

Step1: Substitute \( x = y + 1 \) into \( 3x + 2y = 3 \)

We know \( x = y + 1 \), so substitute \( x \) in the first equation: \( 3(y + 1) + 2y = 3 \)

Step2: Expand and simplify the equation

Expand \( 3(y + 1) \): \( 3y + 3 + 2y = 3 \)
Combine like terms: \( 5y + 3 = 3 \)
Subtract 3 from both sides: \( 5y = 0 \)
Divide by 5: \( y = 0 \)

Step3: Find \( x \) using \( x = y + 1 \)

Substitute \( y = 0 \) into \( x = y + 1 \): \( x = 0 + 1 = 1 \)

Answer:

A. The solution is \((1, 0)\)