Solve systems of equations by using substitution and elimination How to U se Substitution Solve one of the equations for one of the variables Isolate one of the variables in one of the equations ID: 659778
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Slide1
3-2 Solving Systems Algebraically
Solve systems of equations by using substitution and elimination.Slide2
How to U
se 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.Slide3
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)Slide4
Try This
Solve the following system by substituting:
y = 3x and x + y = -32
(-8, -24)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
Elimination
Add or subtract two linear equations in order to eliminate one of the variables.
Look for whichever is easiest to cancel by adding or subtracting.
Answers should still be ordered pairs.Slide8
Practice
2x + 5y = 17
6x – 5y = -9
Cancel 5y using addition.
Now we have 8x = 8
x
= 1
Substitute x = 1 into either equation to find y.
(1, 3)Slide9
You try!
x
+ y = 101
2.5x + y = 164
Use subtraction
Change all the signs of the second equation.
(42, 59)Slide10
Multiplying to Cancel
Anything cancel?
If we were to multiply the second equation by 2, then x would cancel.
So the second equation becomes
or
Use addition
(3, 4)
Slide11
Assignment
Odds p.146 #15-25,31,33,41