Question

system b
line 1: $y=-\frac{1}{2}x+\frac{3}{2}$
line 2: $y=\frac{1}{2}x+\frac{9}{2}$
this system of equations is:
consistent independent
consistent dependent
inconsistent
this means the system has:
a unique solution
solution: (□,□)
no solution
infinitely many solutions

Explanation:

Step1: Set the two equations equal

Since both equal \(y\), we set \(-\frac{1}{2}x+\frac{3}{2}=\frac{1}{2}x+\frac{9}{2}\).

Step2: Solve for \(x\)

Add \(\frac{1}{2}x\) to both sides: \(\frac{3}{2}=x+\frac{9}{2}\). Then subtract \(\frac{9}{2}\) from both sides: \(x=\frac{3}{2}-\frac{9}{2}=- 3\).

Step3: Solve for \(y\)

Substitute \(x = - 3\) into \(y=\frac{1}{2}x+\frac{9}{2}\), so \(y=\frac{1}{2}\times(-3)+\frac{9}{2}=\frac{-3 + 9}{2}=3\).

Answer:

consistent independent; a unique solution; \((-3,3)\)