Question

graph the system of linear equations to approximate the solution.
equation 1: $y = 2x + 4$
equation 2: $y = \frac{1}{2}x + 5$
graph of coordinate plane with y and x axes
a (0, 5)
b (-2, 0)
c $(5\frac{1}{2}, \frac{2}{3})$ (corrected as needed, original may have typo)
d $(\frac{2}{3}, 5\frac{1}{2})$

Explanation:

Step1: Set equations equal

To find the solution, set \(2x + 4=\frac{1}{2}x + 5\).

Step2: Solve for \(x\)

Subtract \(\frac{1}{2}x\) and 4 from both sides:
\(2x-\frac{1}{2}x=5 - 4\)
\(\frac{4x - x}{2}=1\)
\(\frac{3x}{2}=1\)
Multiply both sides by \(\frac{2}{3}\): \(x=\frac{2}{3}\).

Step3: Find \(y\)

Substitute \(x = \frac{2}{3}\) into \(y = 2x+4\):
\(y=2(\frac{2}{3})+4=\frac{4}{3}+\frac{12}{3}=\frac{16}{3}=5\frac{1}{3}\).
So the solution is \((\frac{2}{3},5\frac{1}{3})\), which matches option D.

Answer:

D. \((\frac{2}{3}, 5\frac{1}{3})\)