Solve the system of equations.

3x−4y=40
5x−5y=55(1 point)
Responses

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

(4,−7)
left parenthesis 4 comma negative 7 right parenthesis

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

(18, 7)

1 answer

To solve the system of equations, we can use either the substitution method or the elimination method.

Using the substitution method:
1. Solve one equation for one variable in terms of the other variable.
From the first equation, we can solve for x in terms of y:
3x - 4y = 40
3x = 4y + 40
x = (4y + 40)/3

2. Substitute this expression for x into the second equation.
5x - 5y = 55
5((4y + 40)/3) - 5y = 55
(20y + 200)/3 - 5y = 55
20y + 200 - 15y = 165
5y = -35
y = -7

3. Substitute the value of y back into the expression for x to find x.
x = (4(-7) + 40)/3
x = ( -28 + 40)/3
x = 12/3
x = 4

Therefore, the solution to the system of equations is (4, -7).

The correct response is:
(4,−7)
left parenthesis 4 comma negative 7 right parenthesis