SOLUTION: really need help solve the system of nonlinear equations for x and y. sketch a graph of each equation showing the intersection points of the line and the parabola. x^2 + y=4 an

Question 62716: really need help
solve the system of nonlinear equations for x and y. sketch a graph of each equation showing the intersection points of the line and the parabola. x^2 + y=4 and 2x + y=1 thanks so much
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
really need help
solve the system of nonlinear equations for x and y. sketch a graph of each equation showing the intersection points of the line and the parabola.
x^2 + y = 4 and 2x + y = 1
Solve it like any system, using the elimination method
x^2 + y = 4
2x + y = 1
------------ subtract
x^2 - 2x + 0y = 3; y is eliminated so you have:
x^2 - 2x - 3 = 0
Factor this to:
(x-3)(x+1) = 0
x = +3 and x = -1, the solution to this system
:
To graph this (you know the intersection points will be x=+3 and x=-1 from the above solution)
:
First arrange the equations in the general form (y=)
x^2 + y = 4
y = 4 - x^2
:
2x + y = 1
y = 1 - 2x
:
Write up a table to plot, y = 4 - x^2
Start with x = -5: ie y = 4 - (-5^2) = - 21
:
x | y
-----
-5|-21
-4|-12
-3|-5
-2|0
-1|+3; point of intersection
0 |+4
+2|0
+3|-5; point of intersection
+4|-12
:
Do the same with y = 1 - 2x, it's a straight line so a couple plots will do it
x | y
-----
-3|+7
-1|+3; point of intersection
0 |+1
+1|-1
+3|-5; point of intersection
+4|-7
:
:
Your graph should look this

:
Do you see the relationship between our solutions and the graph intersections?
you can email me if you have a question on this?

RELATED QUESTIONS
Solve the following nonlinear system for x and y. Sketch a graph, showing the... (answered by ichudov)

I need help solving the following nonlinear system of equation: y = x^2 3x = y... (answered by stanbon)

solve the nonlinear system of equations for real solutions x^2+y^2=9 x^2+(y-2)^2=1 (answered by asuar010)

I have a system of nonlinear equations, x^2+y^2=49 y^2-3x=49 I need to find... (answered by advanced_Learner,jorel555)

Solve the following system of nonlinear equations 25x^2+9y^2=225... (answered by Edwin McCravy)

solve nonlinear system of equations for real solutions y=x^2-3... (answered by ankor@dixie-net.com)

Solve the nonlinear system of equations. Solve by using elimination or substitution... (answered by Alan3354)

Solve the following system of nonlinear equations y=-x^2-2x+14... (answered by Fombitz)