Question 1053721
.
4x^2 + 9y^2 = 72
x - y^2 = -1

Select all of the following that are solutions to the system shown.
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<pre>
4x^2 + 9y^2 = 72,   (1)
x - y^2 = -1.       (2)

To solve it algebraically, express y^2 = x+1 from the equation (2) and substitute it into equation (1). You will get

4x^2 + 9(x+1) = 72.

In this way you got a single equation for only one unknown x.

Simplify and solve it:

4x^2 + 9x - 63 = 0,

{{{x[1,2]}}} = {{{(-9 +- sqrt(9^2 + 4*4*63))/(2*4)}}} = {{{(-9 +- 33)/8}}}.

{{{x[1]}}} = {{{24/8}}} = 3,  {{{x[2]}}} = {{{-42/8}}} = -5.25.

The negative root doesn't suit the equation y^2 = x+1, since the right site would be negative.

So, the only solution for x is x=3.

Then you get two solutions for y: y^2 = x+1 = 3+1 = 4 and  {{{y[1]}}} = 2,  {{{y[2]}}} = -2.

<U>Answer</U>. The system has two solutions (x,y) = (3,2)  and  (x,y) = (3,-2).
</pre>

For many other solved similar problems see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Systems-of-equations/Solving-the-system-of-alg-eqns-of-deg2-deg1.lesson>Solving systems of algebraic equations of degree 2 and degree 1</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Systems-of-equations/Solving-the-system-of-algebraic-equations-of-degree-2.lesson>Solving systems of algebraic equations of degree 2</A> 

in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Systems of equations that are not linear</U>".