Systems of equations
By Bradley lenaway
Math is as easy as 1,2,3
Question
• Claire has $54 to buy CD’s and books. Each CD
costs $9, and each book costs $6.she wants to
buy exactly 7 items. Write and solve a system
of equations that could be used to determine
the number of CD’s and the number of books
Claire buys.
Substitution
• One way to solve this
problem is by the
Substitution method, I
am going to use this
method in this slide.
• CD’s- X
• Books- Y
• First you have to solve for Y.
• X+Y=7
(this is how many
items she can buy.)
• 9X+6Y=$54
money she has.)
X+Y=7
-X
Y=-X=7
(how much
Substitution (part 2)
• After getting (Y) you
have to plug it into the
other problem where
(Y) is.
• Then you have to
distribute it
You get this
Y=(-X+7)
9X+6(-X+7)=54
this plugging in the (Y)
9X-6X+42=54
Substitution (part 3)
• After getting (9X6X+42=54) you then
have to solve for (X)
• First subtract 9X-6X
• After doing that you
have to move(42) by
subtracting. Then divide
(-3X) on both sides.
• You should get (4)
9X-6X+42=54
-3x+42=54
-42 -42
-3X= 12
-3X -3X
X=4
Elimination
• You can also get the same
answer by another
method called
Elimination.
• First put your two
equations one on top of
another
• After doing so you then
have to cancel out (Y) or
(X). in this case I'm going
to cancel out (Y) by
multiplying (-6) by the
whole equation.
X+Y=7
9X+6Y=$54
-6(X+Y=7)
Elimination (part 2)
• After multiplying (-6)
you the have to
subtract both equations
• (-6Y) and (6Y) cancel
out. So you get (3X=12)
• You then divide both
sides by (3X)
• And you should get (4)
-
-6X-6Y=42
9X+6Y=54
3X=12
3X 3X
X=4
Graphing
• First you have to find (Y)
for both of the
equations. By
subtracting (X) on both
sides
X+Y=7
-X -X
Y=-X+7
9X+6Y=54
-9X -9X
Graphing (part 2)
• After getting (X) you
have to divide any
equation that has a
number in front of (Y)
by that number to get
(Y) for that equation
6Y=-9X+54
6 6 6
Y=-9/6X+9
Graphing (part 3)
• Then once you have
both equation you plug
it into the graph and the
point at which they
cross (the solution) that
is you answer. Witch is 4
10
8
Solution
6
4
2
-10
-8
-6
-4
-2
2
-4
-6
-8
-10
4
6
8
10
All in all…..
• I think that all of these methods are good but I
have to say that the easiest (in my opinion) is
Elimination. I think this is the best way to do
this because there is a lot less steps there are
into solving the equation.
THE END