Can The System 5 5x+6y=1 5x-2y=-5
Be solved more easily by using the substitution method or the addition method?
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I would probably use the addition method first, as the 5x term in each equation can be made to cancel by subtraction:
(5x + 6y) - (5x - 2y) = (1) - (-5)
(5x - 5x) + (6y + 2y) = 1 + 5
8y = 6
y = 6/8 = .75
The x value can be found by substitution from here, or by addition. I find the substitution easier for this.
Substitution
5x - 2(.75) = -5
5x = -5 + 1.5 = -3.5
x = -3.5/5 = -.7
Addition
(5x + 6y) + 3(5x - 2y) = (1) + 3(-5)
5x(1 + 3) + (6y - 3(2)y) = 1 + (-15)
(5)(4)x + (6y - 6y) = -14
20x = -14
x = -14/20 = -.7
(5x + 6y) - (5x - 2y) = (1) - (-5)
(5x - 5x) + (6y + 2y) = 1 + 5
8y = 6
y = 6/8 = .75
The x value can be found by substitution from here, or by addition. I find the substitution easier for this.
Substitution
5x - 2(.75) = -5
5x = -5 + 1.5 = -3.5
x = -3.5/5 = -.7
Addition
(5x + 6y) + 3(5x - 2y) = (1) + 3(-5)
5x(1 + 3) + (6y - 3(2)y) = 1 + (-15)
(5)(4)x + (6y - 6y) = -14
20x = -14
x = -14/20 = -.7
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