Question

Solve the following system of equations:
x+y=−4
y=x2−6x

Answer 1

We can start by substituting y from the first equation into the second equation:

y = x^2 - 6x

x + y = -4

x + (x^2 - 6x) = -4

x^2 - 5x - 4 = 0

We can solve for x by factoring:

(x - 4)(x + 1) = 0

So x = 4 or x = -1.

If x = 4, then y = -8 from the first equation, and y = 4^2 - 6(4) = -8 from the second equation, so (x,y) = (4,-8) is a solution.

If x = -1, then y = 3 from the first equation, and y = (-1)^2 - 6(-1) = 7 from the second equation, so (x,y) = (-1,3) is another solution.

Therefore, the system of equations has two solutions: (4,-8) and (-1,3).