Question

What is the solution of the following system? {3x + 3y = 10−9x − 9y = −30

Answer 1

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

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

Step 1: Multiply the first equation by 3 and the second equation by 1, so that the coefficients of x in both equations will be equal:

3(3x + 3y) = 3(10) => 9x + 9y = 30 (equation A)
1(-9x - 9y) = 1(-30) => -9x - 9y = -30 (equation B)

Step 2: Add equation A and equation B together to eliminate the y-variable:

(9x + 9y) + (-9x - 9y) = 30 + (-30)
0 = 0

Step 3: Since the resulting equation is 0 = 0, this means that the original equations are dependent, and the system has infinitely many solutions.

Therefore, there is no unique solution to the given system of equations.

Answer 2

[AI-generated answer — Bot GPT 3.5]

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

Using the method of substitution:
1) Solve one equation for one variable in terms of the other.
From the first equation, we have:
3x + 3y = 10
Rearranging, we get:
3y = 10 - 3x
y = (10 - 3x)/3

2) Substitute the expression for the variable into the other equation.
Substituting y in the second equation, we get:
-9x - 9((10 - 3x)/3) = -30

3) Simplify and solve for x.
Multiplying through by 3 to eliminate the fraction, we have:
-27x - 90 + 27x = -90
Simplifying, we get:
-90 = -90
This equation is true for all values of x. There is no unique value for x.

4) Solve for y using the expression obtained in step 1.
Using the expression for y from step 1:
y = (10 - 3x)/3
Substituting any value of x, we get a corresponding value of y.

Therefore, the solution to the system of equations is:
(x, y) = (x, (10 - 3x)/3)

Answer 3

[AI-generated answer — Explain Bot]

To find the solution to the system of equations, we can use the method of substitution or elimination.

Let's start by using the method of substitution:

Step 1: Solve one equation for one variable in terms of the other variable.
From the first equation, we have:
3x + 3y = 10
Rearranging the equation:
3x = 10 - 3y
Dividing both sides by 3:
x = (10 - 3y) / 3

Step 2: Substitute the expression obtained in step 1 into the other equation.
Substituting x in the second equation:
-9x - 9y = -30
-9((10 - 3y) / 3) - 9y = -30
Simplifying:
-30 + 9y - 9y = -30
-30 = -30

Step 3: Evaluate the equation obtained in step 2.
The equation -30 = -30 is always true. This means that the given system of equations is inconsistent, and there is no unique solution.

Hence, there is no solution to the given system of equations.