Question

resolver por sustitución.
solve by substitution.
\

$$\begin{cases} x = 2y + 1 \\\\ -3x + 6y = -3 \\end{cases}$$

\bigcirc one solution: \boxed{\quad}
\bigcirc no solution
\bigcirc infinite number of solutions
question help: \boxed{\text{video}}

Explanation:

Step1: Substitute \( x = 2y + 1 \) into the second equation

We have the second equation \( -3x + 6y = -3 \). Substitute \( x \) with \( 2y + 1 \):
\( -3(2y + 1) + 6y = -3 \)

Step2: Simplify the equation

Expand the left - hand side: \( -6y - 3+6y=-3 \)
Combine like terms: \( (-6y + 6y)-3=-3 \), which simplifies to \( 0 - 3=-3 \), or \( - 3=-3 \)

Since we get a true statement (\( - 3=-3 \)) after substitution, this means that the two equations are dependent (they represent the same line), and there are an infinite number of solutions.

Answer:

Infinite number of solutions