Question

system a
line 1: $y = -\frac{1}{2}x - \frac{3}{2}$
line 2: $y = 2x - 9$
this system of equations is:
\bigcirc consistent dependent
\bigcirc consistent independent
\bigcirc inconsistent
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 $y=y$, equate the two expressions:
$$-\frac{1}{2}x - \frac{3}{2} = 2x - 9$$

Step2: Eliminate fractions

Multiply all terms by 2 to clear denominators:
$$-x - 3 = 4x - 18$$

Step3: Isolate x terms

Move x terms to one side:
$$-3 + 18 = 4x + x$$
$$15 = 5x$$

Step4: Solve for x

Divide both sides by 5:
$$x = \frac{15}{5} = 3$$

Step5: Find y value

Substitute $x=3$ into $y=2x-9$:
$$y = 2(3) - 9 = 6 - 9 = -3$$

Answer:

This system of equations is: consistent independent
This means the system has: a unique solution
Solution: $(3, -3)$