Solving Systems of Equations: 5/x + y - 2/x - y = -1 and 15/x + y + 7/x - y = 10
In this article, we will solve a system of equations involving variables x and y. The system consists of two equations:
Equation 1: 5/x + y - 2/x - y = -1 Equation 2: 15/x + y + 7/x - y = 10
Our goal is to find the values of x and y that satisfy both equations.
Step 1: Simplify the Equations
Let's simplify each equation by combining like terms:
Equation 1: (5 - 2)/x + y(1 - 1) = -1 Equation 1: 3/x = -1
Equation 2: (15 + 7)/x + y(1 - 1) = 10 Equation 2: 22/x = 10
Step 2: Solve for x
We can solve for x in both equations:
Equation 1: 3/x = -1 --> x = -3
Equation 2: 22/x = 10 --> x = 22/10 = 11/5
Since the value of x is not the same in both equations, we can conclude that there is no solution for x. However, we can still find the value of y by substituting one of the values of x into either equation.
Step 3: Solve for y
Let's substitute x = -3 into Equation 1:
5/-3 + y - 2/-3 - y = -1 -5/3 + y + 2/3 - y = -1 -3/3 + y = -1 y = -1 - (-3/3) y = -1 + 1 y = 0
Therefore, the value of y is 0.
Conclusion
In conclusion, the system of equations 5/x + y - 2/x - y = -1 and 15/x + y + 7/x - y = 10 has no solution for x, but the value of y is 0.
