Question

solve the system by graphing.
y = 4x + 2
y = 2x + 3
the solution is (\square, \square).

Explanation:

Step1: Set equations equal

Since \( y = 4x + 2 \) and \( y = 2x + 3 \), set \( 4x + 2 = 2x + 3 \).

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 4x - 2x + 2 = 3 \) → \( 2x + 2 = 3 \).
Subtract 2: \( 2x = 3 - 2 \) → \( 2x = 1 \).
Divide by 2: \( x = \frac{1}{2} \).

Step3: Find \( y \)

Substitute \( x = \frac{1}{2} \) into \( y = 2x + 3 \):
\( y = 2(\frac{1}{2}) + 3 = 1 + 3 = 4 \).

Answer:

\((\frac{1}{2}, 4)\)