Solving the Equation: 2x+1/5=3y-2/7=2x+3y-1/6x
In this article, we will solve the equation 2x+1/5=3y-2/7=2x+3y-1/6x. This equation involves fractions and variables, making it a bit more challenging to solve. But don't worry, we will break it down step by step.
Simplifying the Equation
First, let's simplify the equation by combining like terms:
2x + 1/5 = 3y - 2/7 2x + 3y - 1/6x = 3y - 2/7
Eliminating Fractions
Next, we need to eliminate the fractions in the equation. We can do this by finding the least common multiple (LCM) of the denominators, which are 5, 7, and 6. The LCM is 210.
Multiply both sides of the equation by 210 to eliminate the fractions:
420x + 42 = 630y - 60 420x + 630y - 35x = 630y - 60
Simplifying Further
Now, let's simplify the equation further by combining like terms:
385x + 630y = 82
Solving for x and y
We can solve for x and y by using substitution or elimination methods. Let's use the substitution method.
Rearrange the equation to isolate x:
x = (82 - 630y) / 385
Now, substitute the expression for x into one of the original equations, such as 2x + 1/5 = 3y - 2/7:
2((82 - 630y) / 385) + 1/5 = 3y - 2/7
Simplify and solve for y:
y = 11/7
Now that we have found y, we can find x:
x = (82 - 630(11/7)) / 385 x = 13/7
Final Solution
Therefore, the solution to the equation 2x+1/5=3y-2/7=2x+3y-1/6x is:
x = 13/7 y = 11/7
We have successfully solved the equation!
