I can solve systems of linear equations by using substitution Try This Solve the following system by substituting y 3x and x y 32 8 24 How to U se Substitution Solve one of the equations for one of the variables ID: 655145
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Slide1
6.2 Solving Systems Using Substitution
I can solve systems of linear equations by using substitution.Slide2
Try This
Solve the following system by substituting:
y = 3x and x + y = -32
(-8, -24)Slide3
How to Use Substitution
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.Slide4
Practice
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)Slide5
You Try
Solve the system using substitution
6y + 5x = 10
x
+ 3y = -7
(8, -5)Slide6
Using Systems
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 smallSlide7
Practice
x = -2y + 4
3.5x +7y = 14
Infinitely ManySlide8
Special Systems
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
.Slide9
Assignment
Odds p.375 #11-35