Question

｛x∧2+xy=3/4 x/y+1=3/2

Answer 1

{х^2+ху=3/4
х=(3/2-1)у

{(1/2у)^2+1/2у^2=3/4
х=1/2у

{1/4у^2+1/2у^2=3/4
х=1/2у

{3/4у^2=3/4
х=1/2у

{у=1 или у=-1
х=1/2 или х=-1/2

Answer 2

It appears that you have provided a system of two equations involving the variables x and y. To solve this system, we can use either the substitution method or the elimination method. Let's use the substitution method:

The given equations are:

1. x^2 + xy = 3/4
2. x/y + 1 = 3/2

Step 1: Solve one of the equations for one of the variables. Let's solve Equation 2 for x in terms of y: x/y + 1 = 3/2 x/y = 3/2 - 1 x/y = 1/2 x = (1/2) * y

Step 2: Substitute the expression for x from Step 1 into the other equation (Equation 1): x^2 + xy = 3/4 ((1/2) * y)^2 + ((1/2) * y) * y = 3/4 (1/4) * y^2 + (1/2) * y^2 = 3/4 (1/4 + 1/2) * y^2 = 3/4 (3/4) * y^2 = 3/4

Step 3: Solve for y: y^2 = (3/4) * (4/3) y^2 = 1 y = ±1

Step 4: Find the corresponding values of x using the expression we found for x in terms of y: For y = 1: x = (1/2) * y = (1/2) * 1 = 1/2

For y = -1: x = (1/2) * y = (1/2) * (-1) = -1/2

So, the solutions to the system of equations are: x = 1/2, y = 1 x = -1/2, y = -1

Please double-check the calculations, as there might be a chance of error while transcribing the equations. If you need further assistance or clarification, feel free to ask!