• Support PF! Buy your school textbooks, materials and every day products Here!

Graphing system of equations

  • Thread starter duki
  • Start date
  • #1
264
0

Homework Statement



Solve the system of equations graphically.

Homework Equations



1)
4x - y = 5
y = 4 - 5x^2


2)
2x^2 + y^2 = 33
x^2 - y^2 = 12

The Attempt at a Solution



The answers I got for the intersecting points are:
1)
(1, -1)

And

2)
(+/- 3.7, +/- 1.8)

These are estimates from graphing, but I'm not sure if I'm close... I don't know how to check myself algebraically yet... =/
 

Answers and Replies

  • #2
robphy
Science Advisor
Homework Helper
Insights Author
Gold Member
5,490
720
You should be able to at least substitute your graphically-obtained points into the equations.
 
  • #3
264
0
I did that mostly...

but for the equations like y = 4 - 5x^2, is that the same as saying:

y = 4 - 5(-1)^2?
or would it bet
y = 4 - 5(-1^2)?

for that particular equations here are my points:

x............| y
0 .............4
+/-.89 ......0
+/- 1 ......-1
+/- 2 ......-3
 
  • #4
Integral
Staff Emeritus
Science Advisor
Gold Member
7,198
55
for your first problem you have found a possible solution at (1,-1).

Your equations are:
y= 4x -5
and
y= 4 - 5 x 2

Plugging x = 1 into each of these yields:

y = 4(1) -5 = -1

Thus your point is a solution for this equation.

Repeat for the second equation.

y = 4 - 5(-1) 2 = 4 -5 = -1

Thus your solution works in both equations and is an intersection point.

Do the same thing with your second problem.
 
  • #5
264
0
groovy, good to know i'm on the right path...

could you show me how to solve algebraically (#1)? If you could give me a start I'll work on it and let you know where I get....
 
  • #6
Integral
Staff Emeritus
Science Advisor
Gold Member
7,198
55
In my last post I expressed both equatons of your first problem as y expressed in terms of x. Eliminate y by setting them equal, then solve for x.

y= 4x -5
y = 4 - 5x 2
4x -5 = 4 - 5x 2
5x 2 + 4x - 9 = 0

Can you finish?
 

Related Threads on Graphing system of equations

Replies
6
Views
1K
Top