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Solving System of Linear EquationsElimination Method
Warm-up: solve the linear system by
Eliminationy - 2x = -3y - x = -1
(2,1)
Multiplying one equation
-2x - 5y = 2210x + 3y = 22
(5)(5)( )
-10x - 25y = 11010x + 3y = 22 0 - 22y = 132
- 22y = 132-22 -22
y = -6
-2x - 5y = 22-2x - 5y = 22
-2x - 5(-6) = 22
-2x + 30 = 22- 30 - 30
-2x = -8-2 -2
x = 4
(4, -6)
Your turn!4x + 2y = -10-2x + 3y = 33(2)(2)( )
4x + 2y = -10-4x + 6y = 66
0 + 8y = 56
8y = 568 8
y = 7
4x + 2y = -104x + 2y = -104x + 2(7) = -10
4x + 14 = -10- 14 - 14
4x = -244 4
x = -6
(-6, 7)
Your turn… again!
4x + 10y = 702x - 5y = 25
20y = 20
20 = 20
y = 1
4x + 10y = 70
4x + 10(1) = 70
4x + 10 = 70-10 = -10
4x = 204 4
x = 5
Answer: (5,1)
4x + 10y = 70-4x + 10y = -50-2(2x - 5y = 25)
4x + 10y = 70-4x + 10y = -50
Practice!
2x - y = 9 3x + 4y = -14
Answer: ( 2, -5 )
Hint: multiply the first equation by 4
Multiplying two equations
3x + 5y = 105x + 7y = 10
(5)(5)( )
15x + 25y = 50-15x - 21y = -30
0 + 4y = 20
4y = 204 4
y = 5
3x + 5y = 103x + 5y = 103x + 5(5) = 10
3x + 25 = 10- 25 - 25
3x = -153 3
x = -5
(5, -5)
(-3)(-3)( )
Your Turn!2x - 3y = -113x + 2y = 29
(3)(3)( )
6x - 9y = -33-6x -4y = -580 -13y = -91
-13y = -91-13 -13
y = 7
2x - 3y = -112x - 3y = -112x - 3(7) = -11
2x - 21 = -11+ 21 +21
2x = 102 10
x = 5
(7, 5)
(-2)(-2)( )
Summary: On Solving Linear Systems
(Graphing, Substitution, Elimination Methods)Graphing:
Substitution
Elimination
y = ½x + 1
y = -⅔x
y = 2x - 3y = -3x + 2
y = -½x + 1
y = -5x -1
1.) 2.) 3.)
2x + y = 8y = x - 7
y = 3x - 6 -3x + y = -6
y = x + 4y = 3x
1.) 2.) 3.)
x + 2y = 73x - 2y = 1
8x - 9y = 194x + y = -7
4x - 3y = 113x - 5y = -11
1.) 2.) 3.)
Classwork
8x + 11y = 205x - 11y = -59
2x - 3y = 612x + y = -7
2x - 3y = 5 x + 2y = -1
20x + 3y = 20-20x + 5y = 60
1.) 2.)
3.) 4.)