Question

1. directions: solve the system. (show your work)

\\(\

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

\\)
\\(x = \underline{\quad}\\)\\(y = \underline{\quad}\\)

Explanation:

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

Substitute \( y \) in the first equation: \( 2x - 3(x - 1) = -1 \)

Step2: Simplify the equation

Expand and simplify: \( 2x - 3x + 3 = -1 \) → \( -x + 3 = -1 \)

Step3: Solve for \( x \)

Subtract 3 from both sides: \( -x = -1 - 3 \) → \( -x = -4 \) → \( x = 4 \)

Step4: Solve for \( y \)

Substitute \( x = 4 \) into \( y = x - 1 \): \( y = 4 - 1 = 3 \)

Answer:

\( x = 4 \)
\( y = 3 \)