Transcript Solving Linear Systems by Substitution

7.2 Solving Linear Systems by
Substitution
Objectives:
Use substitution to solve linear systems
Model real life situations using a linear
system.
• Solve one of the equations for one of its
variables.
• Substitute the expression from Step 1 into
the other equation and solve for the other
variable.
• Substitute the value from Step 2 into the
revised equation Step and solve.
• Check the solution in each of the original
equations.
SOLVE THE LINEAR SYSTEM
-X + Y = 1
Rearrange equation so
2X + Y = -2
you have X = or Y =
Y=X+1
Replace Y with X + 1
in second equation
Solve for X
2X + X + 1 = -2
3X + 1 = -2
3X = -3
X = -1
Substitute -1 in for X in one
- (-1) + Y = 1
of the original equations.
1+Y=1
Solve for Y. The point of
Y=0
intersection is X = -1 and Y = 0
Solve the system.
-x + y = 1
2x + y = -2
x + 2y = 4
-x + y = -7
2x + 2y = 3
X – 4y = -1
2x + 6y = 15
x = 2y
An office supply company sells two types of
fax machines. They charge $150 for one
of the machines and $225 for the other. If
the company sold 22 fax machines for a
total of $3900 last month, how many of
each type were sold?
One day at the softball tournament $1590
was collected from the 321 people admitted
to the game. The price of each adult
admission is $6 and the student admission
is $4. How many adults and how many
children were admitted that day?
WARM UP TO ALGEBRA!!!!
A. SOLVE FOR Y.
2X + 4Y = -2
B. SOLVE FOR X.
2Y – X = -7
C. FIND THE SLOPE OF THE LINE THAT
GOES THROUGH THE POINTS (0, 8)
AND (8, 0).