Question

sole the system equations

3x+6y=21
-5x+2y=13

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation for x:
3x + 6y = 21
3x = 21 - 6y
x = (21 - 6y) / 3
x = 7 - 2y

Step 2: Substitute this value of x into the second equation.
-5x + 2y = 13
-5(7 - 2y) + 2y = 13
-35 + 10y + 2y = 13
12y - 35 = 13

Step 3: Simplify and solve for y.
12y = 13 + 35
12y = 48
y = 48/12
y = 4

Step 4: Substitute the value of y back into one of the original equations to solve for x.
3x + 6y = 21
3x + 6(4) = 21
3x + 24 = 21
3x = 21 - 24
3x = -3
x = -3/3
x = -1

Therefore, the solution to the system of equations is x = -1 and y = 4.

Answer 2

[AI-generated answer — Explain Bot]

To solve the system of equations:

Equation 1: 3x + 6y = 21
Equation 2: -5x + 2y = 13

There are a few different methods to solve a system of equations, such as substitution, elimination, or using matrices. In this case, we will solve the system by using the elimination method.

Step 1: Multiply one or both of the equations so that when added, one of the variables will cancel out. Let's eliminate the x variable by multiplying Equation 1 by 5 and Equation 2 by 3:

5(3x + 6y) = 5(21) => 15x + 30y = 105
3(-5x + 2y) = 3(13) => -15x + 6y = 39

Now, we have the following equations:

Equation 3: 15x + 30y = 105
Equation 4: -15x + 6y = 39

Step 2: Add Equation 3 and Equation 4 together to eliminate the x variable:

(15x + 30y) + (-15x + 6y) = 105 + 39
Combine like terms:
15x - 15x + 30y + 6y = 144
36y = 144

Step 3: Solve for y by dividing both sides of the equation by 36:

36y/36 = 144/36
y = 4

Now we have the value of y.

Step 4: Substitute y = 4 back into one of the original equations to solve for x. Let's use Equation 1:

3x + 6(4) = 21
3x + 24 = 21
3x = 21 - 24
3x = -3
x = -1

Therefore, the solution to the system of equations is x = -1 and y = 4.

Answer 3

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

To solve the system of equations:

Step 1: Choose either the substitution or elimination method to solve the system. Let's use the elimination method.

Step 2: Multiply the first equation by 5 and the second equation by 3 to make the coefficients of x in both equations opposites of each other. This will allow us to eliminate the x variable when adding the equations together.

5(3x + 6y) = 5(21)
3(-5x + 2y) = 3(13)

Step 3: Simplify and rewrite the equations.

15x + 30y = 105 (Equation 1)
-15x + 6y = 39 (Equation 2)

Step 4: Add the equations together to eliminate the x variable.

(15x + 30y) + (-15x + 6y) = 105 +39
30y + 6y = 144
36y = 144

Step 5: Solve for y by dividing both sides of the equation by 36.

36y/36 = 144/36
y = 4

Step 6: Substitute the value of y (y = 4) back into one of the original equations to solve for x.

3x + 6(4) = 21
3x + 24 = 21
3x = 21 - 24
3x = -3
x = -1

Step 7: The solution to the system of equations is x = -1 and y = 4.