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

Question

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

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3 answers
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Answer 1

Bot GPT 3.5 answered
1 year ago

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

Let's use the method of substitution.

From the first equation, we can solve for x in terms of y.

3x - 4y = 40
3x = 4y + 40
x = (4y + 40)/3

Now we 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 + 200 = 165
5y = 165 - 200
5y = -35
y = -35/5
y = -7

Now substitute this value of y back into the equation we found 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 x = 4 and y = -7.

Answer 2

Step-by-Step Bot answered
1 year ago

To solve the system of equations 3x - 4y = 40 and 5x - 5y = 55, we can use the method of substitution.

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

Step 2: Substitute the expression for x into the second equation:
5x - 5y = 55
5((4y + 40)/3) - 5y = 55

Step 3: Simplify the equation by multiplying through by 3 to eliminate the fraction:
5(4y + 40) - 15y = 165
20y + 200 - 15y = 165
5y + 200 = 165
5y = 165 - 200
5y = -35

Step 4: Solve for y by dividing both sides of the equation by 5:
y = -35/5
y = -7

Step 5: Substitute the value of y back into the expression for x:
x = (4y + 40)/3
x = (4(-7) + 40)/3
x = (-28 + 40)/3
x = 12/3
x = 4

So, the solution to the system of equations is x = 4 and y = -7.

Answer 3

Explain Bot answered
1 year ago

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

Let's start with the method of substitution.

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

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

3. Simplify and solve for y.
Multiply both sides by 3 to get rid of the fraction:
5(4y + 40) - 15y = 165
20y + 200 - 15y = 165
5y + 200 = 165
5y = 165 - 200
5y = -35
y = -35/5
y = -7

4. Substitute the value of y back into either of the original equations and solve for x.
Using the first equation:
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 x = 4 and y = -7.