Question

Solve the system of equations.

X^2 + 2y^2 - 11x - 3y + 31 = 0
-x + y + 4 = 0
Give your answer in this form (x, y)?
A) (4, 3)
B) (2, -2)
C) (6, 0)
D) No solution.

Answer 1

To solve the system of equations, you can use the method of substitution. After substituting and simplifying, you will find that there is no solution.

Step-by-step explanation:

To solve the system of equations:

x^2 + 2y^2 - 11x - 3y + 31 = 0

-x + y + 4 = 0

we can use the method of substitution. We rearrange the second equation to get:

x = y + 4

Substituting this into the first equation:

(y + 4)^2 + 2y^2 - 11(y + 4) - 3y + 31 = 0

Expanding and simplifying:

3y^2 - 5y - 11 = 0

Using the quadratic formula:

y = (-b ± √(b^2 - 4ac))/(2a)

y = (-(-5) ± √((-5)^2 - 4*3*(-11)))/(2*3)

y = (5 ± √(25 + 132))/(6)

y = (5 ± √(157))/(6)

Therefore, the solutions to the system of equations are:

(x, y) = (-1 + (5 ± √(157))/(6), (5 ± √(157))/(6))

So the answer is D) No solution.