Question

(04.02 lc) solve the following system: y = x + 3 3x + y = 19 (7, 4) (-4, 7) (4, 7) (4, -7)

Explanation:

Step1: Substitute \( y = x + 3 \) into \( 3x + y = 19 \)

Substitute \( y \) in the second equation: \( 3x + (x + 3) = 19 \)

Step2: Simplify and solve for \( x \)

Simplify the equation: \( 3x + x + 3 = 19 \) → \( 4x + 3 = 19 \)
Subtract 3 from both sides: \( 4x = 19 - 3 = 16 \)
Divide by 4: \( x = \frac{16}{4} = 4 \)

Step3: Find \( y \) using \( y = x + 3 \)

Substitute \( x = 4 \): \( y = 4 + 3 = 7 \)

Answer:

C. (4, 7) (assuming the third option is labeled as C; if options are labeled as A, B, C, D with (4,7) as the third, then the answer is the option with (4,7), e.g., if the third option is C. (4, 7), then C. (4, 7))