Solve the following system for all solutions: (x - 1)^2 + (y + 3)^2 = 13 x + y = -3
1 answer:
Answer:
- ( -4, -1 ) and ( -9, - 6)
Step-by-step explanation:
<h3>Given</h3>
- (x - 1)^2 + (y + 3)^2 = 13
-
x + y = -3
<h3>Solution</h3>
<u>From the second equation we get</u>
<u>Substituting x in the first equation</u>
- (- y - 3 - 1)^2 + (y + 3)^2 = 13
- (-y - 4)^2 + (y + 3)^2 = 13
- (y+4)^2 + (y+3)^2 = 13
- y^2 + 8y + 16 + y^2 + 6y + 9 = 13
- 2y^2 + 14y + 12 = 0
- y^2 +7y +6 = 0
- (y+1)(y+6) = 0
- y = - 1
- y = - 6
<u>Then</u>
<u>Answer</u>
- ( -4, -1 ) and ( -9, - 6)
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