Question

line 1: $y = \frac{1}{2}x + 3$
line 2: $y = x + 4$
this system of equations is:
consistent independent
consistent dependent
inconsistent
this means the system has:
a unique solution
solution: (, )
infinitely many solutions
no solution

Explanation:

Step1: Set the two equations equal

Since \(y = \frac{1}{2}x + 3\) and \(y=x + 4\), we set \(\frac{1}{2}x+3=x + 4\).

Step2: Solve for \(x\)

Subtract \(\frac{1}{2}x\) from both sides: \(3=\frac{1}{2}x+4\). Then subtract \(4\) from both sides: \(- 1=\frac{1}{2}x\). Multiply both sides by \(2\) to get \(x=-2\).

Step3: Solve for \(y\)

Substitute \(x =-2\) into \(y=x + 4\). So \(y=-2 + 4=2\).

Answer:

consistent independent; a unique solution; Solution: \((-2,2)\)