Download 6.2 Solving Systems Using Substitution

Solve the following system by
substituting:
y = 3x
and x + y = -32
(-8, -24)
Solve one of the equations for
one of the variables.
Isolate one of the variables in one
of the equations.
Choose whichever seems easiest.
Substitute the expression for the
variable in the other equation.
Use substitution when a system
has at least one equation that
can be solved quickly for one of
the variables.
Solve the following system:
3y + 4x = 14
-2x + y = -3
The second equation looks
easiest to solve for y
So y = 2x – 3
Substitute 2x – 3 for y in the other
equation
3(2x – 3) + 4x = 14
Solve for x
x = 2.3
Now substitute 2.3 for x in either
equation
y = 1.6
The solution is (2.3, 1.6)
Solve the system using
substitution
6y + 5x = 10
x + 3y = -7
(8, -5)
A large snack pack costs $5
and a small costs $3. If 60 snack
packs are sold, for a total of
$220, How many were large and
how many were small?
Let x = large and y = small
Money: 5x + 3y = 220
Amount sold: x + y = 60
Solve: (20, 40)
20 large and 40 small
x = -2y + 4
3.5x +7y = 14
Infinitely Many
When variables cancel and
you are left with a true
statement, there are infinitely
many solutions.
When variables cancel and
you are left with a false
statement, there are no
solutions.
Odds p.375 #11-35