There is a point (x,y) in the first quadrant and on the line 3x-5y=12 for which the x-coordinate is three times the y-coordinate. What is the value of X + Y at that point
We are given that the point (x,y) lies on the line 3x - 5y = 12 and the x-coordinate is three times the y-coordinate. So we can write:
x = 3y
Substituting this into the equation of the line, we get:
3(3y) - 5y = 12
Simplifying this, we get:
4y = 4
So, y = 1
Substituting y = 1 into x = 3y, we get:
x = 3(1) = 3
Therefore, the point (x,y) is (3,1) and the sum of the coordinates is:
X + Y = 3 + 1 = 4
So the value of X + Y at the given point is 4.
The equation 3x-5y=12 can be rearranged to give y=3x/5. Substituting this expression into the given equation x+y=X+Y gives us X+Y=x+3x/5. Solving for x gives us x=(5/2)(X+Y). Since the x-coordinate is three times the y-coordinate, we have 3(X+Y)/5=X+Y, which can be rearranged to give X+Y=15. Therefore, the value of X+Y at the point (x,y) is 15.