Asked by PurPur
6x–5y=27
3x+5y=36
3x+5y=36
Answers
There are no human answers yet.
Answered by
GPT 3.5
To solve this system of equations, we can use the method of elimination.
First, let's multiply the second equation by 2 to make the coefficients of y in both equations opposites:
2(3x + 5y) = 2(36)
6x + 10y = 72
Now, we have:
6x - 5y = 27
6x + 10y = 72
Adding the two equations together, we eliminate the variable x:
(6x - 5y) + (6x + 10y) = 27 + 72
12x + 5y = 99
Now, we can solve for y by subtracting 12x from both sides:
5y = 99 - 12x
5y = 99 - 12x
5y = 99 - 12x
y = 19.8 - 2.4x
Next, we substitute this value of y back into one of the original equations to find x:
3x + 5(19.8 - 2.4x) = 36
3x + 99 - 12x = 36
-9x + 99 = 36
-9x = -63
x = 7
Finally, plug the value of x back into one of the original equations to solve for y:
6(7) - 5y = 27
42 - 5y = 27
-5y = -15
y = 3
Therefore, the solution to the system of equations is x = 7 and y = 3.
First, let's multiply the second equation by 2 to make the coefficients of y in both equations opposites:
2(3x + 5y) = 2(36)
6x + 10y = 72
Now, we have:
6x - 5y = 27
6x + 10y = 72
Adding the two equations together, we eliminate the variable x:
(6x - 5y) + (6x + 10y) = 27 + 72
12x + 5y = 99
Now, we can solve for y by subtracting 12x from both sides:
5y = 99 - 12x
5y = 99 - 12x
5y = 99 - 12x
y = 19.8 - 2.4x
Next, we substitute this value of y back into one of the original equations to find x:
3x + 5(19.8 - 2.4x) = 36
3x + 99 - 12x = 36
-9x + 99 = 36
-9x = -63
x = 7
Finally, plug the value of x back into one of the original equations to solve for y:
6(7) - 5y = 27
42 - 5y = 27
-5y = -15
y = 3
Therefore, the solution to the system of equations is x = 7 and y = 3.
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