Final answer:
To solve the system of equations, rewrite the second equation in terms of x^2 and y^2, substitute the expression from the first equation into the second equation, simplify and solve for x, substitute the values of y into the expression for x and calculate.
Step-by-step explanation:
To solve the system of equations:
1. Rewrite the second equation in terms of x^2 and y^2: x^2 - y^2 = 5
2. Substitute (4x^2 - 9y^2) from the first equation into the second equation:
4x^2 - 9y^2 - y^2 = 5
3. Simplify and solve for x:
4x^2 - 10y^2 = 5
x^2 = (10y^2 - 5)/4
x = ±sqrt((10y^2 - 5)/4)
4. Substitute the values of y into the expression for x and calculate:
x = ±sqrt((10(0)^2 - 5)/4) = ±sqrt(-5/4)
Since the value inside the square root is negative, there are no real solutions for x and y.