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SOLVE THE NONLINEAR SYSTEM OF EQUATIONS FOR REAL SOLUTIONS
 
y =  x2 + 3
 
y = -x2 + 5

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Kathye P. | Math Geek, passionate about teachingMath Geek, passionate about teaching
5.0 5.0 (150 lesson ratings) (150)
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:
 
x+ 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.
 
Ron S. | Expert in Test Prep, Science, and MathExpert in Test Prep, Science, and Math
4.8 4.8 (51 lesson ratings) (51)
1
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)