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Simultaneous Equations
So you ask... what is it?
It is a set of equations
for example...
3x+2y=5
x2y=3
where the values of x and y
in
both equations
are
the same
2
1/2
And no... it's not difficult to solve at all
Today we will learn 3 skills within simultaneous equations.
Graphical Method
Equating Values of y
Problem Solving
The Graphical Solution.
To find the solution graphically...
We graph the equations to find the intercept.
Intercept = Solution
For example
y=3x+2
y=x4
becomes...
y=3x+2
y=x4
(3, 7)
x=3
y=7
Equating Values of y.
Some exercises...
{
This is a much faster than the graphical method.
Consider these equations:
y=x+2
y=2x+5
if y is equal to:
x+2
AND
2x+5
then:
x+2
=
2x+5
minus 2
x
=
2x+3
add 2x
3x
=
3
x=1
If
x=1
then
y=x+2
y=2x+5
{
becomes
{
y=1+2
y=2+5
y=3.
Problem Solving.
These equations are given in words
to solve them, we need to:
interpret the information
into equations
before
solving the equations
FOR EXAMPLE
"two numbers have a
sum
of
15
and a
difference
of
7
.
Find the numbers."
Let
x
and
y
be the unknown numbers.
{
x
+
y=
15
x

y=
7
x+y=15
xy=7
add the equations together
2x =22
x=11.
y=4.
11+y=15
11y=7
If
{
{
{
y = 2x + 3
y = 5x + 2
y = 2x + 1
y = 3x  2
y = x=2
y = x  1
y = x + 4
y = x + 2
{
Some exercises...
{
{
{
y = x + 1
y = 5  x
y = 15  x
y = 2x + 3
y = x  4
y = 22  x
y = x  5
y = 9 + x
Some exercises...
Giselle is 27 years older than her son. 6 years ago, she was 4 times older. What are the present ages of each person?
500 tickets were sold. Adult tickets cost $10.00, children's cost $4.00, and a total of $4112 was collected. How many tickets of each kind were sold?
Some exercises...
two numbers have a sum of 20 and a product of 96
two number have a product of 24 and a difference of 5
two numbers have a quotient of 4 and a sum of 15
Another example:
"Tom has
more
money than George. If Tom gave George
$20
, they would have the
same amount
. If George gave Tom
$22
, Tom would have
twice as much
as Bob. How much money do they each have?"
Tom =
x
George =
y
two numbers have a difference of 5 and when x is doubled, the difference is 14
x20=y+20
{
(as Tom gave George $20, which made their amount equal)
x+22=2(y22)
(as after George gave Tom $22 Tom had twice as much money as George)
x20=y+20
{
x+22=2(y22)
implies that
x=y+40
we substitute the x with its value above
which means:
y+40+22=2y44
y+62=2y44
y2y=4462
y=106
y=106.
as x=y+40
x=146.
A pen contains rabbits and pheasants only. There are 17 heads and 60 feet. How many of each animal does the pen contain?
The graphical method is very precise
but very
time consuming
.
PROS AND CONS
To equate the values of y we first need the equations to be in the form of
y= (expression)
Thank you for watching.
If there are any problems
feel free to read through the instructions again.
DRISHTI, MICHELLE Y., AND DONNA
FROM
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Simultaneous Equations
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