Question

Solve the following system. 4x^2 9y^2 = 72 x^2 - y^2 = 5 list your answers in numerical order by the x-value and then the y-value. remember to include the commas. the solutions are ( ), ( ), ( ), and ( )

Answer 1

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.