Final answer:
In an isosceles trapezoid, the legs are congruent, so by setting the expressions for the lengths of legs AB and CD equal to each other and solving for y, we find that the value of y is 7.
Step-by-step explanation:
To find the value of y in an isosceles trapezoid ABCD where the legs AB and CD are given by the equations AB = 4y - 3 and CD = 5y - 10, and the base BC is given by the equation BC = 3y - 4, we need to use the property that in an isosceles trapezoid the legs are congruent, which means AB = CD. Setting the equations for AB and CD equal to each other gives us:
4y - 3 = 5y - 10
Solving for y, we subtract 4y from both sides:
-3 = y - 10
We then add 10 to both sides:
7 = y
Therefore, the value of y is 7.