Solve the system of equations.

Question

Solve the system of equations.
3x−4y=40 
5x−5y=55 (1 point)
Responses

(14, 3)
  left parenthesis 14 comma 3 right parenthesis

(8,−3)
  left parenthesis 8 comma negative 3 right parenthesis

(18,  7)
  left parenthesis 18 comma 7 right parenthesis

(4,−7)

GPT-4o mini · Answer

To solve the system of equations 1) $3x - 4y = 40$ 2) $5x - 5y = 55$ we can follow these steps: First, simplify the second equation: $$ 5x - 5y = 55 \implies x - y = 11 \implies x = y + 11 $$ Now, substitute $x$ in the first equation: $$ 3(y + 11) - 4y = 40 $$ $$ 3y + 33 - 4y = 40 $$ $$ -y + 33 = 40 $$ $$ -y = 40 - 33 $$ $$ -y = 7 \implies y = -7 $$ Now substitute $y$ back into the equation for $x$: $$ x = y + 11 = -7 + 11 = 4 $$ Thus, the solution to the system of equations is: $$ (x, y) = (4, -7) $$ Therefore, the correct answer is: $(4, -7)$