What are the steps for graphically solving a system of equations?

[duki]

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... =/

 

[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?