Evaluate when x = 2, y = -5, z = 3.
x^2 - y = 3
3z - 4(y + 1) - y^2 = 0
x - yz = -13
(2)^2-1(-5)
4+ 5 = 9
3(3) -4(-5+1)-(5)^2
9 + 16 -25 =0
2-(-5)(3)
2-(-15)
2+ 15 = 17
To evaluate when x = 2, y = -5, and z = 3, substitute these values into each equation and simplify.
1. Evaluating the equation x^2 - y = 3:
Replace x with 2 and y with -5:
2^2 - (-5) = 3
4 + 5 = 3
9 = 3
Therefore, when x = 2, y = -5, and z = 3, the equation x^2 - y = 3 does not hold true.
2. Evaluating the equation 3z - 4(y + 1) - y^2 = 0:
Replace z with 3, y with -5, and simplify:
3(3) - 4(-5 + 1) - (-5)^2 = 0
9 + 4(4) - 25 = 0
9 + 16 - 25 = 0
25 - 25 = 0
0 = 0
Therefore, when x = 2, y = -5, and z = 3, the equation 3z - 4(y + 1) - y^2 = 0 holds true.
3. Evaluating the equation x - yz = -13:
Replace x with 2, y with -5, z with 3, and simplify:
2 - (-5)(3) = -13
2 + 15 = -13
17 = -13
Therefore, when x = 2, y = -5, and z = 3, the equation x - yz = -13 does not hold true.
In summary, out of the three equations given, only one of them holds true when x = 2, y = -5, and z = 3.