2x-3y 2=x 2y-5=3x y?
To solve this system of equations, we will use the method of substitution.
1) Start with the equation 2x - 3y = 2.
2) Solve for x by adding 3y to both sides: 2x = 3y + 2.
3) Divide both sides by 2: x = (3y + 2)/2.
Now, substitute this value of x into the second equation: 2y - 5 = 3x.
4) Substitute the value of x from step 3 into the second equation: 2y - 5 = 3((3y + 2)/2).
5) Simplify the equation: 2y - 5 = (3/2)(3y + 2).
Now we can solve for y by multiplying both sides of the equation by 2 to clear the fraction:
6) 2(2y - 5) = 2(3/2)(3y + 2).
7) Distribute the 2 on the left side: 4y - 10 = 3(3y + 2).
8) Distribute the 3 on the right side: 4y - 10 = 9y + 6.
9) Combine like terms by subtracting 9y from both sides: -5y - 10 = 6.
10) Add 10 to both sides: -5y = 16.
11) Divide both sides by -5: y = 16/-5.
Therefore, the value of y is y = -16/5 or -3.2.