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 (4,−7) left parenthesis 4 comma negative 7 right parenthesis (18, 7)

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

Let's use the substitution method:

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

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

Substitute y back into the first equation 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).

Answer 2

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

To solve the system of equations:

3x - 4y = 40 ...(Equation 1)
5x - 5y = 55 ...(Equation 2)

We'll use the method of substitution to find the values of x and y.

Step 1: Solve one of the equations for one variable.
Let's solve Equation 1 for x.
Rearrange Equation 1 to solve for x:
3x = 4y + 40
x = (4y + 40)/3 ...(Equation 3)

Step 2: Substitute the expression for x from Equation 3 into Equation 2.
Replace x in Equation 2 with (4y + 40)/3:
5(4y + 40)/3 - 5y = 55

Step 3: Simplify and solve for y.
Multiply through by 3 to eliminate the fraction:
5(4y + 40) - 3(5y) = 165
20y + 200 - 15y = 165
5y + 200 = 165
5y = 165 - 200
5y = -35
y = -35/5
y = -7

Step 4: Substitute the value of y back into Equation 3 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).

Answer 3

[AI-generated answer — Explain Bot]

To solve the system of equations, we will use the method of substitution. Here's how you can do it:

Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the first equation (3x - 4y = 40) for x:
3x - 4y = 40
3x = 40 + 4y
x = (40 + 4y)/3

Step 2: Substitute one equation into the other.
Replace x in the second equation (5x - 5y = 55) with the expression we found in step 1:
5((40 + 4y)/3) - 5y = 55

Step 3: Simplify and solve for y.
This equation can be simplified by multiplying through by 3 to get rid of the fractions:
5(40 + 4y) - 15y = 165
200 + 20y - 15y = 165
5y = 165 - 200
5y = -35
y = -35/5
y = -7

Step 4: Substitute the value of y back into one of the original equations to solve for x.
Let's use the first equation (3x - 4y = 40):
3x - 4(-7) = 40
3x + 28 = 40
3x = 40 - 28
3x = 12
x = 12/3
x = 4

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