math help???????

Question

SOLVE THE NONLINEAR SYSTEM OF EQUATIONS FOR REAL SOLUTIONS

 

y =  x² + 3

 

y = -x² + 5

Answer 1

Hi, Mario!

 

Solve the system of equations using substitution. Since both equations are already in the "y=" form, we can set x²+3 equal to -x²+5:

 

x² + 3 = -x² + 5  

 

Rearrange the terms:    

 

2x² = 2

 

Solving, we get that x = 1 or x = -1. But we are not done yet! Solving the system means getting x and y values.

 

We can plug the values we found for x into either of the original equations. I recommend trying both equations just to make sure that your answers do work in both.

 

We get y=4 for both x=1 and x=-1 in both equations. So the solution is (1,4) and (-1,4).

 

Hope this helps!

Kathye P.

 

Answer 2

You can set the two expressions for y equal to each other and get

 

x² + 3 = -x² +5 which simplifies to

2x² = 5 - 3 = 2 so

x² = 1 and

x = ±1

 

plugging this into either of the equations yields y = 4

 

so these two quadratics intersect at (±1, 4)