Question

Решите систему x^2-3y =-9 x+y=3

Answer 1

Решение на фотографии

Answer 2

We can solve this system of equations using substitution.

From the second equation, we have:

y = 3 - x

Substituting this expression for y into the first equation, we get:

x^2 - 3(3 - x) = -9

Expanding and simplifying, we get:

x^2 - 9 + 3x = -9

Moving all terms to one side, we get:

x^2 + 3x - 9 = 0

Now we can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 3, and c = -9.

Plugging in these values, we get:

x = (-3 ± sqrt(3^2 - 4(1)(-9))) / 2(1)

Simplifying, we get:

x = (-3 ± sqrt(69)) / 2

So the solutions for x are:

x = (-3 + sqrt(69)) / 2, x = (-3 - sqrt(69)) / 2

Now we can use either equation to solve for y. Let's use the second equation:

x + y = 3

Substituting our values for x, we get:

(-3 + sqrt(69)) / 2 + y = 3

Solving for y, we get:

y = 3 - (-3 + sqrt(69)) / 2

Simplifying, we get:

y = (9 + sqrt(69)) / 2

So the solutions for the system are:

x = (-3 + sqrt(69)) / 2, y = (9 + sqrt(69)) / 2

and

x = (-3 - sqrt(69)) / 2, y = (9 - sqrt(69)) / 2