What value of z would make the expressions equivalent? (1 point) 4x - 5y and (3y + 2x) - z(4y - x)
To find the value of z that would make the expressions equivalent, we set them equal to each other and solve for z.
4x - 5y = (3y + 2x) - z(4y - x)
Expanding the expression on the right side:
4x - 5y = 3y + 2x - 4zy + zx
Rearranging and combining like terms:
4x - 2x - 5y - 3y = zx - 4zy
2x - 8y = z(x - 4y)
Now we can set the coefficients of the variables on both sides equal to each other:
2 = z
x - 4y = -8y
Solving the second equation for x:
x = -8y + 4y
x = -4y
Substituting the value of x in the first equation:
2 = z
Therefore, the value of z that would make the expressions equivalent is 2.