Question

graph the system below and write its solution.\

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

\
note that you can also answer
o solution\ or \infinitely many\ solutions.

Explanation:

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

Substitute the expression for \( y \) from the first equation into the second equation. So we have \( x + 2(-3x - 2)=1 \).

Step2: Simplify the equation

First, distribute the 2 in \( 2(-3x - 2) \): \( x - 6x - 4 = 1 \). Then combine like terms: \( -5x - 4 = 1 \).

Step3: Solve for \( x \)

Add 4 to both sides: \( -5x = 1 + 4 \), so \( -5x = 5 \). Divide both sides by -5: \( x = \frac{5}{-5} = -1 \).

Step4: Solve for \( y \)

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

Answer:

The solution is \( x = -1 \), \( y = 1 \) (or the ordered pair \((-1, 1)\))