Solve Nonlinear Systems By Addition
Solve the system by the addition method.
-$x ^ { 2 } - y ^ { 2 } = 25$
$16 x ^ { 2 } + 25 y ^ { 2 } = 400$
A) $\{ ( 5,0 ) , ( - 5,0 ) \}$
B) $\{ ( 4,0 ) , ( - 4,0 ) \}$
C) $\{ ( 0,5 ) , ( 0 , - 5 ) \}$
D) $\{ ( 0,4 ) , ( 0 , - 4 ) \}$

Question

Quizplus · Accepted Answer

We can solve this system by using the addition method, which means we need to add the two equations together in order to eliminate one of the variables. However, the equations are not currently set up to be added together easily. So, we need to manipulate one or both of the equations to make them easier to add.

One way to do this is to multiply the first equation by 16, which will give us a 16x^2 term that we can add to the second equation:

$16x^2 - 16y^2 = 400$
$16x^2 + 25y^2 = 400$

Now we can add the equations together and eliminate the x^2 term:

$-16y^2 + 25y^2 = 0$

So, we have y^2 = 0 or y^2 = 25. If y^2 = 0, then y = 0 and we can substitute this into either equation to get x = ±5. If y^2 = 25, then y = ±5 and we can substitute this into either equation to get x = 0.

Therefore, the solution is {(5,0), (-5,0)}, which corresponds to choice A.

Solve Nonlinear Systems by Addition Solve the System by the Addition

Solve Nonlinear Systems by Addition
Solve the System by the Addition