Question

solve the system by the addition method.
3x + 5y = 28
3x + 2y = 40
a. {(-16,3)}
b. {(-16,5)}
c. {(16,-4)}
d. {(-4,16)}
question list
question 1
question 2
question 3
question 4
question 5

Explanation:

Step1: Label the equations

Let the first equation be \( 3x + 5y = 28 \) (Equation 1) and the second equation be \( 3x + 2y = 40 \) (Equation 2).

Step2: Subtract the equations

Subtract Equation 2 from Equation 1 to eliminate \( x \):

$$
LATEXBLOCK0
$$

Step3: Solve for \( y \)

Divide both sides by 3:

$$ y = \frac{-12}{3} = -4 $$

Step4: Substitute \( y \) into Equation 2

Substitute \( y = -4 \) into \( 3x + 2y = 40 \):

$$
LATEXBLOCK1
$$

Answer:

C. \(\{(16, -4)\}\)