Systems of equations
By Bradley lenaway
Math is as easy as 1,2,3
Question
• Clair has $54 to buy CD’s and books. Each CD
costs $9, and each book costs $6.she wants to
by 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.
Substation
• One way to solve this
problem is by the
substation 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
Substation (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
Substation (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