What value of z would make the expressions 4x−5y and (3y+2x)−z(4y−x) equivalent?

Question

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Answer 1

To find the value of z that would make the two expressions equivalent, we need to set them equal to each other and solve for z.

4x - 5y = (3y + 2x) - z(4y - x)

Let's simplify the equation:

4x - 5y = 3y + 2x - (4yz - zx)
4x - 5y = 3y + 2x - 4yz + zx (Distribute the negative sign)
-5y = 3y + zx - 4yz (Combine like terms)
-5y - 3y = zx - 4yz (Move terms involving y to one side)
-8y = zx - 4yz (Combine like terms)

We want the expressions to be equal, so the coefficients of x, y, and z on both sides should be the same.

From the equation -8y = zx - 4yz, we can see that the coefficient of x on the right side is z, and the coefficient of y is 4z.

For the expressions to be equal, the coefficient of x on the left side (which is 0) must be equal to z. Therefore, the value of z is 0.

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