What value of z would make the expressions 4x−5y and (3y+2x)−z(4y−x) equivalent?
To find the value of z that would make the expressions 4x - 5y and (3y + 2x) - z(4y - x) equivalent, we can set the two expressions equal to each other:
4x - 5y = (3y + 2x) - z(4y - x)
Simplify both sides of the equation:
4x - 5y = 3y + 2x - 4zy + zx
Rearrange the terms:
4x - 2x - 5y - 3y = -4zy + zx - 4xy
Combine like terms:
2x - 8y = z(-4y + x - 4x)
Divide both sides by -4y + x - 4x:
(2x - 8y) / (-4y + x - 4x) = z
Simplify the denominator:
(2x - 8y) / (-4y - 3x) = z
Therefore, the value of z that would make the two expressions equivalent is (2x - 8y) / (-4y - 3x).
so whats the answer
The answer is (2x - 8y) / (-4y - 3x).
the 2 equations are a fraction together
I apologize for the misunderstanding. If the two expressions are meant to be fractions, let's rewrite them accordingly:
First expression: (4x - 5y)
Second expression: [(3y + 2x) - z(4y - x)]
To find the value of z that would make these two fractions equivalent, we need to set them equal to each other:
(4x - 5y) = [(3y + 2x) - z(4y - x)]
To simplify, we can distribute the negative sign through z(4y - x):
4x - 5y = 3y + 2x - 4zy + zx
Now, let's isolate the terms involving z on one side of the equation:
4zy + zx = 2x - 3y - 4x + 5y
Combining like terms gives us:
xz + 4zy = -2x + 2y
Factoring out z:
z(x + 4y) = -2x + 2y
Now, divide both sides by (x + 4y) to solve for z:
z = (-2x + 2y) / (x + 4y)
Therefore, the value of z that would make the two fractions equivalent is (-2x + 2y) / (x + 4y).
To find the value of z that would make the expressions 4x−5y and (3y+2x)−z(4y−x) equivalent, we need to set these two expressions equal to each other and solve for z.
Step 1: Set the two expressions equal to each other:
4x−5y = (3y+2x)−z(4y−x)
Step 2: Simplify the equation:
Distribute the -z into the second expression:
4x−5y = 3y+2x−4zy+zx
Group like terms:
(4x−5y) = (2x−4zy)+(3y+zx)
Step 3: Now, compare the coefficients of the variables on both sides of the equation.
For x:
On the left side, the coefficient of x is 4.
On the right side, the coefficient of x is 2−4z.
So, we can equate these two values:
4 = 2−4z
Step 4: Solve for z:
Add 4z to both sides of the equation to isolate the term with z:
4+4z = 2
Subtract 4 from both sides:
4z = -2
Finally, divide both sides by 4 to solve for z:
z = -2/4
Simplifying the equation further:
z = -1/2
Hence, the value of z that would make the expressions 4x−5y and (3y+2x)−z(4y−x) equivalent is z = -1/2.