Objectives:
1. Be able to solve a system of equations by using the substitution
method.
2. Be able to solve a system of equations by using the elimination
method.
Critical Vocabulary:
System of Equations, Elimination
Daily Warm Up: Solve the following system of equations by substitution
-2x + 2y = 4
2x + y = 5
I. Elimination (Standard Form)
Example 4: Solve the system of equations
-2x + 2y = 4
2x + y = 5
3y = 9
3 3
y=3
2x + (3) = 5
- 3 -3
2x = 2
2 2
x=1
-2x + 2(3) = 4
-2x + 6 = 4
- 6 -6
-2x = -2
-2 -2
x=1
Solution: (1, 3)
If two equations are in
standard form a system
can be solved by
ELIMINATION instead
of SUBSTITUTION.
Since both x-terms are
opposites of each other
(-2x and +2x), you can just
add the equations together
to ELIMINATE the “x”
Solve for “y”
Substitute into ONE of
the original equations
Write your solution
I. Elimination (Standard Form)
Example 5: Solve the system of equations
3x + 5y = 25
-3x - 10y = 55
Since both x-terms are
opposites of each other
(-3x and +3x), you can just
add the equations together
to ELIMINATE the “x”
-5y = 80
-5 -5
y = -16
Solve for “y”
3x + 5(-16) = 25
3x - 80 = 25
+ 80 +80
3x = 105
3
3
x = 35
Solution: (35, -16)
Substitute into ONE of
the original equations
Write your solution
I. Elimination (Standard Form)
Example 6: Solve the system of equations
3x - 4y = 7
2x - y = 3
Multiply By -4
3x - 4y = 7
-8x + 4y = -12
-5x = -5
-5 -5
x=1
-8(1) + 4y = -12
-8 + 4y = -12
+8
+8
4y = -4
4
4
y = -1
3(1) - 4y = 7
3 - 4y = 7
-3
-3
2(1) - y = 3
-4y = 4
-4 -4
-y = 1
-1 -1
y = -1
y = -1
Solution: (1, -1)
2-y=3
-2
-2
There or no opposites
here to ELIMINATE,
but if you multiply
everything in equation
2 by negative four you
will have a -4y and +4y.
Substitute into ONE of
the original equations
I. Elimination (Standard Form)
Example 7: Solve the system of equations
-5x + 3y = 10
3x - 2y = -8
Multiply By 2
Multiply By 3
-10x + 6y = 20
9x - 6y = -24
-1x = -4
-1 -1
x=4
3(4) - 2y = -8
12 - 2y = -8
-12
-12
-2y = -20
-2
-2
y = 10
-5(4) + 3y = 10
9(4) - 6y = -24
-10(4) + 6y = 20
-20 + 3y = 10
+20
+20
3y = 30
3 3
36 - 6y = -24
-36
-36
-6y = -60
-6 -6
y = 10
y = 10
-40 + 6y = 20
+40
+40
6y = 60
-6 -6
y = 10
Solution: (4, 10)
Standard 5.1 Solving Systems Homework #2
1. x + y = 4
x - y = -10
6. x = 3y + 30
3y + x = 12
2. x + 3y = 3
x + 6y = 3
7. y = x - 9
x + 8y = 0
3. 2x - 3y = 0
3x - 2y = 5
8. -x + 4y = -20
3x - 12y = 48
4. 2x + 6y = 4
3x - 7y = 6
9. 3x + 6y = 8
-6x + 3y = 2
5. -4x + y = -8
-12x + 3y = -24
10. 2x + 5y = 8
5x - 6y = -1