Transcript Solving Systems - MathLessonSharing

Solving Systems
Using Substitution
x  y  45
x  12
•Now
that aasecond
equation
has been
•Identify
solution
to the
added,
how
can
you
determine
a
equation above!
solution that works for both equations?
•How
many
solutions
are to
there?
•How many
solutions
are there
this
system?
x  y  45
x  12
• Replace x in the first equation with the value of x
given in the second equation
x  y  45
(12)  y  45
y  33
The solution to the
system is (12,33)
Justify by substituting
solution into both equations
x  y  32
x  y 8
•Now
that aasecond
equation
has been
•Identify
solution
to the
added,
how
can
you
determine
a
equation above!
solution that works for both equations?
•How many solutions are there?
x  y  32
x  y 8
What
canvalue
youofdo
• Replace x in the first equation
with the
x
given in the second equationto find out the
x  y  32
( y  8)  y  32
2 y  8  32
2 y  24
y  12
value of x?
x=y+8
x=(12)+8
x=20
2 x  y  26

x  y  5
2 x  y  26
2( y  5)  y  26
2 y  10  y  26
3 y  10  26
3 y  36
y  12
x  y 5
x  (12)  5
x7
Justify by substituting
solution into both
equations!
2 x  y  24

x

y

6

2 x  y  24
x  y6
2( y  6)  y  24
2 y  12  y  24
3 y  12  24
3 y  36
y  12
x  (12)  6
x6
Justify by substituting
solution into both
equations!
3x  2 y  21

 y  2x  4
3 x  2 y  21
3x  2(2 x  4)  21
y  2x  4
y  2(13)  4
3x  4x  8  21 y  26  4
y  30
 x  8  21 Justify by substituting
solution into both
 x  13
x  13 equations!
3x  2 y  2

y


2
x

8
 2x  y  8
3x  2 y  2
3x  2(2 x  8)  2
y  2 x  8
y  2(2)  8
3x  4x 16  2 y  4  8
y4
7 x 16  2 Justify by substituting
solution into both
7 x  14
equations!
x2
 y  4 x  8

y

3
x

5

The U.S. Treasury is thinking about creating 2
new coins, the “google” and the “osand”. One
osand is equal to $.10 less than three googles.
Five osands and five googles have a total value
of $2.50.
Write a system of equations to represent this
situation. Use substitution to solve the system
and determine the value of an osand and a
google.