Final answer:
To solve the equation 3x = 4y, we need to plug in the given relationships and solve for the variables. In scenarios (a), (b), and (c), both x and y must equal 0 for the equations to be valid. For scenario (d), the solution provides x as 51.43 degrees and y as 38.57 degrees.
Step-by-step explanation:
The student asked to find the value of each variable when "3x" degrees are equal to "4y" degrees. To solve this, we need to set 3x equal to 4y and solve for one variable in terms of the other.
Solution for (a) x = y
Since 3x = 4y, if x equals y, substituting y for x gives us 3y = 4y. This equation suggests that y must be 0 in order for the equality to hold true. Thus, if x = y, then both x and y are 0 degrees.
Solution for (b) x = 4y
Substitute 4y for x in 3x = 4y yields 3(4y) = 4y, or 12y = 4y. To find a solution, we would divide both sides by 4y, but this leads to an inconsistency unless y is 0. Thus, like in (a), both variables must be 0 for the equation to be true when x = 4y.
Solution for (c) y = 3x
For y = 3x, substituting 3x for y in 3x = 4y yields 3x = 4(3x), which simplifies to 3x = 12x. This equation only holds true when x = 0, and thus y must also be 0.
Solution for (d) x = 90 - y
Substituting 90 - y for x in 3x = 4y leads to 3(90 - y) = 4y, which simplifies to 270 - 3y = 4y. Adding 3y to both sides gives 270 = 7y, and dividing each side by 7 results in y = 38.57 degrees (to 2 decimal places), and x is found by substituting y back into x = 90 - y, which gives x as 51.43 degrees (to 2 decimal places).