# Graphing system of equations

## Homework Statement

Solve the system of equations graphically.

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

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
Staff Emeritus
Gold Member
for your first problem you have found a possible solution at (1,-1).

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.

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
Staff Emeritus