given that y-1/x +2=1/3 and y+3/3x-1 =5/2 find x and y.am not getting the right answer it should be 1,2.
(y-1)/(x +2) = 1/3. Change to
y - 1 = x/3 + 2/3
(y + 3)/(3x -1) = 5/2 Change to
y + 3 = 15x/2 -5/2
4 = 45 x/6 - 2x/6 -15/6 -4/6
43x/6 = 43/6
x = 1
y -1 = 1/3 + 2/3 = 1
y=2
To solve the given system of equations:
1. Start with the first equation: (y-1)/(x + 2) = 1/3
Cross-multiply to eliminate fractions: 3(y-1) = x+2
Expand and simplify: 3y - 3 = x + 2
Rearrange the equation: x = 3y - 5
2. Move to the second equation: (y + 3)/(3x - 1) = 5/2
Cross-multiply to eliminate fractions: 2(y + 3) = 5(3x - 1)
Expand and simplify: 2y + 6 = 15x - 5
Rearrange the equation: 15x = 2y + 11
3. Substitute the value of x from Equation 1 into Equation 2:
15(3y - 5) = 2y + 11
Simplify and solve for y: 45y - 75 = 2y + 11
Rearrange the equation: 43y = 86
Solve for y: y = 2
4. Substitute the value of y back into Equation 1 to find x:
x = 3(2) - 5
Simplify: x = 6 - 5
Solve for x: x = 1
Therefore, the solution to the system of equations is x = 1 and y = 2.