systems of nonlinear equations

i need to help i have tried this problem but i cannot find the right answer i need to determine the real solutions for this:

x^2+4xy=10
4x^2-xy=6

graph x^2+4xy-10

To solve the system of nonlinear equations, we can use a method called substitution. Here's how you can approach the problem:

Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the first equation, x^2 + 4xy = 10, for x in terms of y:
x^2 = 10 - 4xy
x = √(10 - 4xy)

Step 2: Substitute the value of x into the second equation.
Replace x in the second equation, 4x^2 - xy = 6, with the expression we found in Step 1:
4(√(10 - 4xy))^2 - xy = 6
16(10 - 4xy) - xy = 6
160 - 64xy - xy = 6
160 - 65xy = 6

Step 3: Simplify and solve for the remaining variable.
Rearrange the equation to solve for xy:
-65xy = 6 - 160
-65xy = -154
xy = 154/65
xy = 2.37 approx.

Step 4: Substitute the value of xy back into either equation to solve for x or y.
Let's substitute xy = 2.37 into the first equation, x^2 + 4xy = 10:
x^2 + 4(2.37) = 10
x^2 + 9.48 = 10
x^2 = 10 - 9.48
x^2 = 0.52
x = ±√0.52
x ≈ ±0.72

So, the system of nonlinear equations has two real solutions:
(x, y) ≈ (0.72, 2.37) and (x, y) ≈ (-0.72, 2.37).