Transcript The Substitution Method

The Substitution Method
Solve:
We can solve
an equation
with one
Variable:
Substitution Method
y y  xy 7
y

x

7
y
5 x  
7 x3 7 x  13
5   x  7   3x  13
5x  35  3x  13
2x  35  13
35
35
2x  22  2
x  11
Don’t forget to
solve for y:
y    11  7
4
Answer the
question:
x  11
y4
Substitution: No Solution
Solve the following system of equation algebraically:
2 x  2 y  18
x  3 y
2  3  y   2 y  18
6  2 y  2 y  18
6  18
FALSE
No Solution.
The two lines are
parallel. They
never intersect.
The Hills are Alive
A gondola conductor charges $2 for each yodeler and $1 for each xylophone.
It costs $40 for an entire club, with instruments, to ride the gondola. Two
yodelers can share a xylophone, so the number of yodelers on the gondola
is twice the number of xylophones. How many yodelers and how many
xylophones are on the gondola?
x: Number of xylophones from the club to ride the gondola
y: Number of yodelers from the club to ride the gondola
x  2  2x   40
x  4x  40
5x  40
5
5
x 8
x  2 y  40
y  2x
2x
y  2 8  16
8,16
The solution can be written as a
coordinate point
Check in BOTH
equations
8  2 16  40
40  40
good
16  2 8
16  16
good