Question

Solve the system equation

3x-4y=40
5x-5y=55

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations:

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

We can use the method of substitution or the method of elimination.

Using the method of substitution:

From equation (1), we solve for x in terms of y:
3x = 40 + 4y
x = (40/3) + (4/3)y

Substituting this expression for x into equation (2), we get:
5(40/3 + (4/3)y) - 5y = 55

Multiplying through by 3 to clear the fraction:
200 + 20y - 15y = 165

Simplifying:
5y = -35
y = -7

Now we substitute this value of y into equation (1) to solve for x:
3x - 4(-7) = 40
3x + 28 = 40
3x = 12
x = 4

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

Answer 2

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

To solve the system of equations:

Step 1: Multiply the first equation by 5 and the second equation by 3 to make the coefficients of the x terms the same:

(5)(3x - 4y) = (5)(40)
(3)(5x - 5y) = (3)(55)

This simplifies the equations to:

15x - 20y = 200
15x - 15y = 165

Step 2: Subtract the second equation from the first equation to eliminate the x term:

(15x - 20y) - (15x - 15y) = 200 - 165
15x - 20y - 15x + 15y = 35

Simplifying further:

-5y + 15y = 35
10y = 35
y = 35/10
y = 3.5

Step 3: Substitute the value of y back into one of the original equations and solve for x.

Let's use the first equation:

3x - 4(3.5) = 40
3x - 14 = 40
3x = 40 + 14
3x = 54
x = 54/3
x = 18

Therefore, the solution to the system of equations is x = 18 and y = 3.5.

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:

Step 1: Solve one equation for one variable in terms of the other variable.
We'll solve the first equation for x:
3x - 4y = 40

Adding 4y to both sides of the equation:
3x = 40 + 4y

Dividing by 3:
x = (40 + 4y) / 3

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

Simplifying:
(200 + 20y) / 3 - 5y = 55

Step 3: Solve for y.
Multiplying both sides of the equation by 3 to eliminate the fraction:
200 + 20y - 15y = 165

Combining like terms:
200 + 5y = 165

Subtracting 200 from both sides:
5y = -35

Dividing by 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 - 4(-7) = 40

Simplifying:
3x + 28 = 40

Subtracting 28 from both sides:
3x = 12

Dividing by 3:
x = 4

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