Question

In the system shown below, what are the coordinates of the solution that lies in quadrant IV?

Answer 1

Answer:

The coordinates of the solution that lies in quadrant IV are (2, -5)

Step-by-step explanation:

We have 2 equations, the first of an ellipse and the second of a circumference.

$2x^2+y^2=33\\x^2+y^2+2y=19$

To solve the system solve the second equation for x and then substitute in the first equation

$x^2+y^2+2y=19\\\\x^2 = 19 -y^2 -2y$

So Substituting in the first equation we have

$x^2 = 19 -y^2 -2y\\\\2(19 -y^2 -2y)+y^2=33\\\\38 -2y^2-4y +y^2 = 33\\\\-y^2-4y+5=0\\\\y^2 +4y-5 = 0$

Now we must factor the quadratic expression.

We look for two numbers that multiply as a result -5 and add them as result 4.

These numbers are -1 and 5.

Then the factors are

$y^2 +4y-5 = 0\\\\(y-1)(y+5) = 0$

Therefore the system solutions are:

$y = 1$; $y = -5$

In the 4th quadrant the values of x are positive and the values of y are negative.

So we take the negative value of y and substitute it into the system equation to find x

$y=-5\\\\2x^2+(-5)^2=33\\\\2x^2 = 33-25\\\\2x^2 = 8\\\\x^2 = 4$

$x = 2$, and $x= -2$

In the 4th quadrant the values of x are positive

So we take the positive value of x

the coordinates of the solution that lies in quadrant IV are (2, -5)

Answer 2

Answer:(-2,-5)

Step-by-step explanation:

APEX