Here are my answers. Can you check if I got the right answers? Thank you!
Solve for z:
4x+10yx=0
z=-2x/5y
y^2+3yz-8z-4x=0
z=(-y^2+4x)/(3y-8)
there was no z in your first equation, from you answer I can tell it should have been 4x + 10yz = 0
If so, the answer is right.
last one is right
To solve the equation 4x + 10yx = 0, let's check if the answer z = -2x/5y is correct.
To verify this, we substitute the value of z back into the equation and simplify:
4x + 10yx = 0
4x + 10y(-2x/5y) = 0
4x - 4x = 0
Since both sides of the equation cancel out, we can conclude that z = -2x/5y is the correct solution for the given equation.
Now, let's move on to the second equation: y^2 + 3yz - 8z - 4x = 0.
To check if the answer z = (-y^2 + 4x)/(3y - 8) is correct, we substitute the value of z back into the equation and simplify:
y^2 + 3y((-y^2 + 4x)/(3y - 8)) - 8((-y^2 + 4x)/(3y - 8)) - 4x = 0
Simplifying, we get:
y^2 - 3y^3/(3y - 8) + 8y^2 - 32x/(3y - 8) - 4x = 0
To further simplify, we need to find a common denominator for the fractions:
(y^2(3y - 8) - 3y^3 + 8y^2(3y - 8) - 32x)/(3y - 8) - 4x = 0
Expanding and combining similar terms, we have:
(3y^3 - 8y^2 - 3y^3 + 24y^2 - 32x)/(3y - 8) - 4x = 0
Simplifying further, we get:
(16y^2 - 32x)/(3y - 8) - 4x = 0
Since both sides are not equal, we can conclude that z = (-y^2 + 4x)/(3y - 8) is not the correct solution for the given equation.
Please double-check the calculations to find the correct solution for the second equation.