Solve Nonlinear Systems By Addition
-$$x ^ { 2 } + y ^ { 2 } = 145$$
$x ^ { 2 } - y ^ { 2 } = - 17$
A) $\{ ( 8,9 ) , ( - 8,9 ) , ( 8 , - 9 ) , ( - 8 , - 9 ) \}$
B) $\{ ( 8,9 ) , ( 9,8 ) , ( - 8 , - 9 ) , ( - 9 , - 8 ) \}$
C) $\{ ( 8 , - 9 ) , ( 8,9 ) \}$
D) $\{ ( - 8 , - 9 ) , ( - 9 , - 8 ) \}$

Question

Quizplus · Accepted Answer

Adding the two equations $x^2 + y^2 = 145$ and $x^2 - y^2 = -17$ eliminates $y^2$, resulting in $2x^2 = 128$, or $x^2 = 64$, giving $x = \pm 8$. Substituting $x = 8$ into the first equation gives $y^2 = 81$, so $y = \pm 9$. Thus, all combinations of $x = \pm 8$ and $y = \pm 9$ are solutions, which matches choice A.

Solve Nonlinear Systems by Addition - x2+y2=145x ^ { 2 } + y ^ { 2 } = 145x2+y2=145

Solve Nonlinear Systems by Addition
- $x ^ { 2 } + y ^ { 2 } = 145$