The solutions to the system of equations are given as follows: (1, -3) and (-4,2).
What is a system of equations?
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The equations are given as follows:
- (x + 3)² + (y + 2)² = 17.
From the second equation:
y = -2 - x.
Replacing in the first:
(x + 3)² + (y + 2)² = 17.
(x + 3)² + (-2 - x + 2)² = 17
x² + 6x + 9 + x² = 17
2x² + 6x - 8 = 0
2(x² + 3x - 4) = 0
2(x + 4)(x - 1) = 0.
Then the solutions for x are:
The solutions for y are:
- When x = 1, y = -2 - 1 = -3.
- When x = -4, y = -2 -(-4) = 2.
Hence the solutions are:
(1, -3) and (-4,2).
More can be learned about a system of equations at https://brainly.com/question/24342899
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