Solving Systems of Linear Equations
In this article, we will solve a system of linear equations involving two variables x and y.
Equation 1: 3/x + y + 2/x - y = 2
Let's simplify the first equation:
3/x + y + 2/x - y = 2
Combine like terms:
(3/x + 2/x) + y - y = 2
Simplify:
5/x = 2
Cross-multiply:
5 = 2x
Divide by 2:
x = 5/2
Equation 2: 9/x + y - 4/x - y = 1
Let's simplify the second equation:
9/x + y - 4/x - y = 1
Combine like terms:
(9/x - 4/x) + y - y = 1
Simplify:
5/x = 1
Cross-multiply:
5 = x
Divide by 1:
x = 5
Solving for y
Now that we have found x, we can substitute x into one of the original equations to solve for y. Let's use Equation 1:
3/x + y + 2/x - y = 2
Substitute x = 5/2:
3/(5/2) + y + 2/(5/2) - y = 2
Simplify:
12/5 + y - y = 2
Simplify:
12/5 = 2
Subtract 12/5 from both sides:
y = 2 - 12/5
Simplify:
y = (-2)/5
Solution
The solution to the system of linear equations is:
x = 5
y = (-2)/5
Therefore, the values of x and y that satisfy both equations are x = 5 and y = (-2)/5.
