Solve the system of equations.

Question

Solve the system of equations.

6x - 5y = 27

3x + 5y = 36 (1 point)

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3 answers
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Answer 1

Bot GPT 3.5 answered
1 year ago

Adding the two equations together, we have:

(6x - 5y) + (3x + 5y) = 27 + 36

Combining like terms, we get:

9x = 63

Dividing both sides of the equation by 9, we find:

x = 7

Substituting this value into the second equation, we have:

3(7) + 5y = 36

21 + 5y = 36

Subtracting 21 from both sides, we get:

5y = 15

Dividing both sides of the equation by 5, we find:

y = 3

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

Answer 2

Step-by-Step Bot answered
1 year ago

To solve the system of equations:

Step 1: Multiply the first equation by 3 to eliminate the terms with "x" when added to the second equation:
3 * (6x - 5y) = 3 * 27
18x - 15y = 81

Step 2: Add the modified equations together:
(18x - 15y) + (3x + 5y) = 81 + 36
18x - 15y + 3x + 5y = 117

Step 3: Combine like terms:
21x - 10y = 117

Step 4: Divide the equation by 21 to isolate "x":
(21x - 10y) / 21 = 117 / 21
x - (10/21)y = 9/7

Step 5: Multiply the second equation by 2 to eliminate the terms with "y" when added to the first equation:
2 * (3x + 5y) = 2 * 36
6x + 10y = 72

Step 6: Add the modified equations together:
(6x + 10y) + (6x - 15y) = 72 + 81
6x + 10y + 6x - 15y = 153

Step 7: Combine like terms:
12x - 5y = 153

Now we have two equations:
x - (10/21)y = 9/7
12x - 5y = 153

This is a system of linear equations where we can solve for the values of "x" and "y".

Answer 3

Explain Bot answered
1 year ago

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

First, let's multiply the second equation by -2 to eliminate the term "5y":

-2(3x + 5y) = -2(36)
-6x - 10y = -72

Now, we have the system of equations:

6x - 5y = 27
-6x - 10y = -72

Adding these two equations together will eliminate the variable "x":

(6x - 5y) + (-6x - 10y) = 27 + (-72)
-5y - 10y = -45

Simplifying the left side gives:

-15y = -45

To solve for "y", divide both sides of the equation by -15:

-15y / -15 = -45 / -15
y = 3

Now that we have the value of "y", we can substitute it back into either of the original equations to find the value of "x". Let's use the first equation:

6x - 5(3) = 27
6x - 15 = 27

Add 15 to both sides to isolate "x":

6x - 15 + 15 = 27 + 15
6x = 42

Divide both sides by 6 to solve for "x":

6x / 6 = 42 / 6
x = 7

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