2x+5y=9,3x+2y=6

x=3

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Asked 11/3/2008 8:19:50 AM

Updated 6/30/2023 6:57:37 PM

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To solve the system of equations:

2x + 5y = 9 ...(1)

3x + 2y = 6 ...(2)

There are multiple methods to solve this system, but I will use the method of substitution. Here's how:

From equation (2), solve for x in terms of y:

3x = 6 - 2y

x = (6 - 2y) / 3

Substitute this value of x in equation (1):

2((6 - 2y) / 3) + 5y = 9

Now, we can simplify and solve for y:

(12 - 4y) / 3 + 5y = 9

12 - 4y + 15y = 27

11y = 15

y = 15 / 11

Substitute the value of y back into equation (2) to find x:

3x + 2(15 / 11) = 6

3x + 30 / 11 = 6

3x = 6 - 30 / 11

3x = (66 - 30) / 11

3x = 36 / 11

x = 12 / 11

Therefore, the solution to the system of equations is:

x = 12 / 11

y = 15 / 11

2x + 5y = 9 ...(1)

3x + 2y = 6 ...(2)

There are multiple methods to solve this system, but I will use the method of substitution. Here's how:

From equation (2), solve for x in terms of y:

3x = 6 - 2y

x = (6 - 2y) / 3

Substitute this value of x in equation (1):

2((6 - 2y) / 3) + 5y = 9

Now, we can simplify and solve for y:

(12 - 4y) / 3 + 5y = 9

12 - 4y + 15y = 27

11y = 15

y = 15 / 11

Substitute the value of y back into equation (2) to find x:

3x + 2(15 / 11) = 6

3x + 30 / 11 = 6

3x = 6 - 30 / 11

3x = (66 - 30) / 11

3x = 36 / 11

x = 12 / 11

Therefore, the solution to the system of equations is:

x = 12 / 11

y = 15 / 11

Added 6/30/2023 6:57:37 PM

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