Question

What is one of the solutions to the following system of equations? x2 + y2 = 9 y − x = 3 Group of answer choices (3, 0) (0, 3) (−3, 1) (1, −3)

Answer 1

One of the solutions to the given system of equations is (0, 3) or (-3, 0).

Step-by-step explanation:

Given the system of equations:

x2 + y2 = 9

y - x = 3

We can solve the second equation for y:

y = 3 + x

Substituting this value of y into the first equation:

x2 + (3 + x)2 = 9

Simplifying:

x2 + 9 + 6x + x2 = 9

Combining like terms:

2x2 + 6x + 9 = 9

2x2 + 6x = 0

Factoring out 2x:

2x(x + 3) = 0

Setting each factor equal to zero and solving for x:

2x = 0 --> x = 0

x + 3 = 0 --> x = -3

So the solutions to the system of equations are (0, 3) and (-3, 0).