Transcript Document

Systems
of
Equations
We will be looking systems of two equations and two
variables, but the equations will not be strictly of
lines. Remember that when we find the solutions,
they are the (x, y) that work in both equations and
geometrically that means they are the points that are
on both graphs, meaning the points of intersection of
the graphs.
Let’s look at the graphs of these equations:
This is a basic
parabola moved up 1
This is a line with
slope 4 and y int. 1
y  x 1
y  4x 1
2
These graphs intersect in two
places so when we algebraically
solve this we can expect two
answers.
y  x 1
2
y  4x 1
(4, 17)
These equations would be easy
to solve with substitution. The
sub
inysub
herein here
first equation tells us
what
yinfind y
equals so let’s sub itto
infind
for yto
(0, 1)
the second equation.
2
This is a quadratic equation so
get everything on one side = 0
and factor if possible.
2
x 1  4x 1
x  4x  0
x  0,
xx  4  0
y 1
x4
y  17
x  y  10
y  x  2 A line with slope 1 and y int. 2
2
2
A circle centered at (0, 0) with
radius square root of 10
Let’s identify and graph each of these equations.
What do they look like?
From the second equation we
know what y equals so let’s sub
it in the first equation.
x  x  2  10
2
2
FOIL this
x  x  4 x  4  10
2
2
x  y  10 x  x  4 x  4  10
2
2x  4x  6  0
y  x2
2
2
2

2

2 x  2x  3  0
2
2x  3x  1  0
x  3, x  1
y  1 y  3
(1, 3)
(-3, -1)
Acknowledgement
I wish to thank Shawna Haider from Salt Lake Community College, Utah
USA for her hard work in creating this PowerPoint.
www.slcc.edu
Shawna has kindly given permission for this resource to be downloaded
from www.mathxtc.com and for it to be modified to suit the Western
Australian Mathematics Curriculum.
Stephen Corcoran
Head of Mathematics
St Stephen’s School – Carramar
www.ststephens.wa.edu.au