Question

Solve the system of equations.

3x−4y=40
5x−5y=55 (1 point)
Responses

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

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

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

(8,−3)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we can use the method of substitution. We can solve one equation for one variable and substitute it into the other equation.

From the first equation, we can solve for x:
3x - 4y = 40
3x = 4y + 40
x = (4y + 40)/3

Substituting x into the second equation:
5((4y + 40)/3) - 5y = 55
(20y + 200)/3 - 5y = 55
20y + 200 - 15y = 165
5y = -35
y = -7

Substituting y back into x = (4y + 40)/3:
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).

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

We are given the following equations:
1) 3x - 4y = 40
2) 5x - 5y = 55

From equation 1, let's solve for x:
3x - 4y = 40
3x = 4y + 40
x = (4y + 40)/3

Now, substitute this value of x into equation 2:
5((4y + 40)/3) - 5y = 55

Multiply both sides of the equation by 3 to eliminate the fraction:
5(4y + 40) - 15y = 165
20y + 200 - 15y = 165
5y + 200 = 165
5y = 165 - 200
5y = -35
y = -35/5
y = -7

Now, substitute the value of y back into equation 1 to find x:
3x - 4(-7) = 40
3x + 28 = 40
3x = 40 - 28
3x = 12
x = 12/3
x = 4

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

Answer 3

[AI-generated answer — Explain Bot]

To solve the system of equations, we can use the method of substitution or the method of elimination. Let's use the method of substitution.

1. Start with the first equation: 3x - 4y = 40. Solve for x in terms of y by isolating x:
3x = 4y + 40
Divide both sides by 3:
x = (4y + 40)/3

2. Substitute this expression for x into the second equation:
5x - 5y = 55
5((4y + 40)/3) - 5y = 55
Multiply 5 by (4y + 40)/3:
(20y + 200)/3 - 5y = 55
Multiply through by 3 to eliminate the fraction:
20y + 200 - 15y = 165
Simplify:
5y + 200 = 165
Subtract 200 from both sides:
5y = -35
Divide both sides by 5:
y = -7

3. Now that we have the value of y, we can substitute it back into the first equation to solve for 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).