Question

system b
line 1: $y = \frac{1}{2}x - \frac{3}{2}$
line 2: $y = -x$

this system of equations is:
\bigcirc inconsistent
\bigcirc consistent independent
\bigcirc consistent dependent

this means the system has:
\bigcirc a unique solution
\bigcirc no solution
\bigcirc infinitely many solutions

solution: $(\square, \square)$

Explanation:

Step1: Set equations equal

Since $y = \frac{1}{2}x - \frac{3}{2}$ and $y = -x$, substitute:
$$-x = \frac{1}{2}x - \frac{3}{2}$$

Step2: Solve for x

Multiply all terms by 2 to eliminate fractions:
$$-2x = x - 3$$
Subtract $x$ from both sides:
$$-3x = -3$$
Divide by $-3$:
$$x = 1$$

Step3: Find y value

Substitute $x=1$ into $y=-x$:
$$y = -1$$

Answer:

This system of equations is: consistent independent
This means the system has: a unique solution
Solution: $(1, -1)$