Question

Solve for the system of equations

6x-5y=27

3x+5y=36

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

First, let's add the two equations together to eliminate the y variable:

(6x - 5y) + (3x + 5y) = 27 + 36
9x = 63
Divide both sides by 9:
x = 7

Now substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:

6(7) - 5y = 27
42 - 5y = 27
Subtract 42 from both sides:
-5y = -15
Divide both sides by -5:
y = 3

So the solution to the system of equations is x = 7 and y = 3.

Answer 2

[AI-generated answer — Explain Bot]

To solve the given system of equations:

Step 1: Choose one of the equations and solve for one variable in terms of the other variable.
Let's choose the second equation in this case:
3x + 5y = 36
Subtract 3x from both sides:
5y = 36 - 3x
Divide both sides by 5:
y = (36 - 3x) / 5

Step 2: Substitute this expression for y in the other equation and solve for x.
Substitute the expression (36 - 3x) / 5 for y in the first equation:
6x - 5((36 - 3x) / 5) = 27
Multiply both sides by 5 to eliminate the fraction:
30x - 36 + 3x = 27
Combine like terms:
33x - 36 = 27
Add 36 to both sides:
33x = 63
Divide both sides by 33:
x = 63 / 33

Step 3: Simplify the resulting value for x.
x = 63 / 33 = 3 / 11

Step 4: Substitute the value of x into either of the original equations to solve for y.
Let's use the first equation:
6x - 5y = 27
Substitute x = 3/11:
6(3/11) - 5y = 27
Multiply both sides by 11 to eliminate the fraction:
18 - 55y = 297
Subtract 18 from both sides:
-55y = 279
Divide both sides by -55:
y = 279 / -55

Simplifying the value of y:
y = -279 / 55 = -51 / 11

Therefore, the solution to the given system of equations is x = 3/11 and y = -51/11.

Answer 3

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

To solve this system of equations, we will use the method of substitution.

First, let's solve one of the equations for one variable in terms of the other variable. Let's solve the second equation for x:

3x + 5y = 36

Subtract 5y from both sides:

3x = 36 - 5y

Next, divide both sides by 3 to solve for x:

x = (36 - 5y) / 3

Now, substitute the value of x in the first equation:

6((36 - 5y) / 3) - 5y = 27

Simplify the equation:

2(36 - 5y) - 5y = 27

Expand and distribute:

72 - 10y - 5y = 27

Combine like terms:

-15y + 72 = 27

Now, isolate the variable by subtracting 72 from both sides:

-15y = 27 - 72

Simplify:

-15y = -45

Finally, divide both sides by -15 to solve for y:

y = -45 / -15

Simplify:

y = 3

Now, substitute this value of y back into one of the original equations to solve for x. Let's use the second equation:

3x + 5(3) = 36

Multiply:

3x + 15 = 36

Subtract 15 from both sides:

3x = 36 - 15

Simplify:

3x = 21

Finally, divide both sides by 3 to solve for x:

x = 21 / 3

Simplify:

x = 7

Therefore, the solution to the system of equations is x = 7 and y = 3.