Question

line 1: $y = -dfrac{1}{2}x - dfrac{5}{2}$
line 2: $y = 2x + 5$
this system of equations is:
\bigcirc inconsistent
\bigcirc consistent independent
\bigcirc consistent dependent
this means the system has:
\bigcirc a unique solution
solution: (\square, \square)

Explanation:

Step1: Set equations equal

Since $y=y$, equate the two expressions:
$$-\frac{1}{2}x - \frac{5}{2} = 2x + 5$$

Step2: Eliminate fractions

Multiply all terms by 2:
$$-x - 5 = 4x + 10$$

Step3: Isolate x terms

Move x terms to one side:
$$-x - 4x = 10 + 5$$
$$-5x = 15$$

Step4: Solve for x

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

Step5: Solve for y

Substitute $x=-3$ into $y=2x+5$:
$$y = 2(-3) + 5 = -6 + 5 = -1$$

Answer:

This system of equations is: consistent independent
This means the system has: a unique solution
Solution: $(-3, -1)$