evaluate x²(xy-x) for x satisying (13x-6)/4 = 5x+1 and y satisfying 12-y=7(y+4)+1
To evaluate x²(xy-x) for x and y satisfying the given equations, we will first solve the equations to find the values of x and y. Then we substitute those values into the expression x²(xy-x) to get the final answer.
Let's solve the equations step by step:
Equation 1: (13x-6)/4 = 5x+1
To solve this equation, we'll start by multiplying both sides by 4 to get rid of the denominator:
4 * (13x-6)/4 = 4 * (5x+1)
This simplifies to:
13x - 6 = 20x + 4
Next, we'll rearrange the equation by moving the variable terms to one side and the constant terms to the other side:
13x - 20x = 4 + 6
-7x = 10
Now, we'll isolate x by dividing both sides by -7:
x = 10 / -7
Simplifying further, we get:
x = -10/7
Equation 2: 12 - y = 7(y+4) + 1
Let's simplify this equation step by step:
Start by distributing the 7 on the right side:
12 - y = 7y + 28 + 1
Combine like terms on the right side:
12 - y = 7y + 29
Next, rearrange the equation:
-y - 7y = 29 - 12
-8y = 17
Now, divide both sides by -8:
y = 17 / -8
Simplifying further:
y = -17/8
Now that we have the values of x and y, let's substitute them into the expression x²(xy-x):
Substituting x = -10/7 and y = -17/8, we get:
(-10/7)²((-10/7)(-17/8)-(-10/7))
Now, let's simplify this expression further:
(-10/7)²((-10/7)(-17/8)+10/7)
Calculating the numerator of the first term within the square:
(-10/7)² = (100/49)
Calculating the numerator of the second term within the square:
((-10/7)((-17/8)) + 10/7)
=((-10/7)(34/8) + 70/49)
=(-340/56 + 70/49)
Finding a common denominator for the terms:
= ((-340/56)(7/7) + (70/49)(8/8))
=(-2380/392 + 560/392)
Combining the terms:
=(-2380 + 560)/392
=(-1820)/392
Finally, simplifying the fraction:
=(-455/98)
Therefore, x²(xy-x) = -455/98.