Question

two linear equations are shown.
what is the solution to the system of equations?
(7, 4)
(9, 7)
(7, \frac{13}{3})
(8, \frac{14}{3})

Explanation:

Step1: Set equations equal

The system is \( y = \frac{1}{3}x + 2 \) and \( y = \frac{4}{3}x - 5 \). Set them equal: \(\frac{1}{3}x + 2 = \frac{4}{3}x - 5\).

Step2: Solve for x

Subtract \(\frac{1}{3}x\) from both sides: \(2 = x - 5\). Add 5 to both sides: \(x = 7\).

Step3: Find y

Substitute \(x = 7\) into \(y = \frac{1}{3}x + 2\): \(y = \frac{1}{3}(7) + 2 = \frac{7}{3} + \frac{6}{3} = \frac{13}{3}\).

Answer:

\((7, \frac{13}{3})\)