factories 3x-2y=5 and xy=2 them find the value of 27x3-8y3
Answers
Step-by-step explanation:
First, use the simultaneous equation method to find x and y by letting the first equation be 3x - 2y = 5 and the second equation be xy = 6.
3x - 2y = 5 (1st equation)
xy = 6 (2nd equation)
In the 2nd equation, move y over to 6 by dividing.
x = \frac{6}{y}
y
6
Then, substitute x into the 1st equation.
3(\frac{6}{y}
y
6
) - 2y = 5
Move 2y over to 5.
3(\frac{6}{y}
y
6
) = 5 + 2y
Multiply 3 with the numerator of the fraction, 6.
\frac{18}{y}
y
18
= 5 + 2y
Move the y on the left side of the equation to the right and multiply.
18 = y(5 + 2y)
18 = 5y + 2y²
Leave the equation in general form by letting the values equal to 0.
2y² + 5y - 18 = 0
Factorise the equation.
(y - 2)(2y + 9) = 0
Solve for the values of y.
y - 2 = 0
y = 2
2y + 9 = 0
2y = -9
y = -9/2
Substitute the values of y into the 2nd equation and solve for x.
x(2) = 6
2x = 6
x = 3
x(-9/2) = 6
x = 6 ÷ -9/2
x = 6 × -2/9
x = -4/3