To solve the system of equations:
1) xy = 122) 3/x - 1/y = 5/12
We can start by rearranging the second equation to isolate y:
3/x - 1/y = 5/12Multiply through by xy (which equals 12):
3y - x = 53y = x + 5y = (x + 5) / 3
Now, substitute this y value into the first equation:
x[(x + 5)/3] = 12x(x + 5) = 36Expanding and rearranging:
x^2 + 5x - 36 = 0(x + 9)(x - 4) = 0
This gives us two possible values for x: x = -9 or x = 4
Substitute these back into the equation for y to find the corresponding values:
1) For x = -9:y = (-9 + 5) / 3y = -4 / 3
2) For x = 4:y = (4 + 5) / 3y = 9 / 3y = 3
Therefore, the solutions to the system of equations are: (-9, -4/3) and (4, 3)
To solve the system of equations:
1) xy = 12
2) 3/x - 1/y = 5/12
We can start by rearranging the second equation to isolate y:
3/x - 1/y = 5/12
Multiply through by xy (which equals 12):
3y - x = 5
3y = x + 5
y = (x + 5) / 3
Now, substitute this y value into the first equation:
x[(x + 5)/3] = 12
x(x + 5) = 36
Expanding and rearranging:
x^2 + 5x - 36 = 0
(x + 9)(x - 4) = 0
This gives us two possible values for x: x = -9 or x = 4
Substitute these back into the equation for y to find the corresponding values:
1) For x = -9:
y = (-9 + 5) / 3
y = -4 / 3
2) For x = 4:
y = (4 + 5) / 3
y = 9 / 3
y = 3
Therefore, the solutions to the system of equations are: (-9, -4/3) and (4, 3)