If x/y=4, x-y=9, and y-x=-9, what is x & y?
x/y=4, means x=4y
substitute 4y for x in x-y=9
to get
(4y)-y = 9
Can you continue?
Note: the third equation (y-x)=-9 can be derived from the second (x-y)=9, so it gives no new information.
3y
To solve for x and y in the given equations, we can use a method called simultaneous equations or system of equations.
1. Start by rearranging the equations:
Equation 1: x/y = 4
Equation 2: x - y = 9
Equation 3: y - x = -9
2. To eliminate the fractions in Equation 1, cross multiply:
x = 4y
3. Substitute this value of x into Equations 2 and 3:
Equation 2 becomes (4y) - y = 9, which simplifies to 3y = 9
Equation 3 becomes y - (4y) = -9, which simplifies to -3y = -9
4. Solve for y by dividing both sides of Equation 2 and Equation 3 by 3:
3y/3 = 9/3, which gives y = 3
-3y/-3 = -9/-3, which gives y = 3
We find that y = 3 in both cases, which confirms the consistency of the equations.
5. Now, substitute the value of y (which is 3) back into the equation x = 4y:
x = 4(3), which yields x = 12
Therefore, the solution to the given system of equations is x = 12 and y = 3.