(y-5)%3D0-y-2%2Fx%2By-8%3D3.jpeg "(x-6)(y-5)=0 Y-2/x+y-8=3")
Solving the System of Equations
In this article, we will solve a system of equations involving two variables, x and y.
Equation 1: (x-6)(y-5)=0
To solve this equation, we can start by factoring the left-hand side:
$(x-6)(y-5)=0$
This tells us that either (x-6) = 0 or (y-5) = 0.
Solving for the first factor, we get:
$x-6=0 \Rightarrow x=6$
And solving for the second factor, we get:
$y-5=0 \Rightarrow y=5$
So, we have found two possible solutions: x = 6 and y = 5.
Equation 2: y - 2/x + y - 8 = 3
To solve this equation, we can start by isolating the terms involving y:
$y - \frac{2}{x} + y - 8 = 3$
Combine like terms:
$2y - \frac{2}{x} - 8 = 3$
Add 8 to both sides:
$2y - \frac{2}{x} = 11$
Now, we can try to solve for y. However, we notice that the equation involves a fraction, which can make it difficult to solve. Let's try to eliminate the fraction by multiplying both sides by x:
$2xy - 2 = 11x$
Now, let's rearrange the equation to isolate y:
$y = \frac{11x + 2}{2x}$
We can substitute the values of x we found earlier (x = 6) into this equation to find the corresponding values of y:
$y = \frac{11(6) + 2}{2(6)} = \frac{68}{12} = \frac{17}{3}$
So, we have found another possible solution: x = 6 and y = 17/3.
Conclusion
In conclusion, we have solved the system of equations and found two possible solutions: (x, y) = (6, 5) and (x, y) = (6, 17/3).
