1. Explain how to apply elimination in solving a system of equations.
2. Explain how to apply substitution in solving a system of equations.
3. Demonstrate each technique in solving the system
1. 3x + 9y = 12
2. 5x - 4y = 3
Admire
Favorite Answer
Explain by demonstration
Substitution
From 1, x = (12 - 9y)/3 = 4 - 3y.....Put this in '2'
5(4 - 3y) - 4y = 3
20 - 15y - 4y = 3
19y = 17
y = 17/19
x = 4 - 3*17/19 = 25/19
Elimination
Eliminate x by multiplying '1' by 5 and '2' by 3 to get
15x + 45y = 60
15x - 12y = 9 ...Now Subtract
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0x + 57y = 51
y = 51/57 = 17/19....Put this in '1'
3x + 9*17/19 = 12
3x = 12 - 153/19 = 75/19
x = 75/19 * 1/3 = 25/19
(25/19, 17/19)
Juan
3x + 9y = 12
9y = 12 - 3x
3y = 4 - x
y = (4 - x) / 3
5x - 4y = 3
-4y = 3 - 5x
4y = 5x - 3
y = (5x - 3) / 4
(4 - x) / 3 = (5x - 3) / 4
4 * (4 - x) = 3 * (5x - 3)
16 - 4x = 15x - 9
16 = 19x - 9
25 = 19x
x = (25/19)
3*(25/19) + 9y = 12
(75/19) + 9y = 12
(75/19) + 9y = (228/19)
9y = (153/19)
y = (17/19)
5 * (25/19) - 4y = 3
(125/19) - 4y = 3
(125/19) - 4y = (57/19)
-4y = -68/19
4y = 68/19
y = (17/19)
x = (25/19); y = (17/19) or [(25/19),(17/19)]