Graphing system of equations

duki

1. The problem statement, all variables and given/known data

Solve the system of equations graphically.

2. Relevant equations

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


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

3. 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... =/

robphy

You should be able to at least substitute your graphically-obtained points into the equations.

duki

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

Integral

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.

duki

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....

Integral

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?