Could You Please Help Me With These Two Problems? Thank You!
Solve by the elimination method 1. X+2y=22 -x+3y=18 2. Solve by substitution method 9m+n=74 m-8n=65
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1. Add the two equations together.
(x + 2y) + (-x + 3y) = (22) + (18) (this eliminates the x variable)
5y = 40 (collect terms)
y = 40/5 = 8 (divide both sides by 5)
x + 2(8) = 22 (substitute 8 for y in the first equation)
x = 22 - 16 = 6 (subtract 16 from both sides)
(x, y) = (6, 8)
2. Solve the first equation for n.
n = 74 - 9m (subtract 9m from both sides)
Substitute this into the second equation.
m - 8(74-9m) = 65
m - 8*74 + 72m = 65 (apply the distributive property)
73m = 65 + 592 (add 8*74 to both sides)
m = 657/73 = 9 (divide both sides by 73)
Substitute this answer back into our equation for n.
n = 74 - 9(9) = 74 - 81 = -7
(m, n) = (9, -7)
(x + 2y) + (-x + 3y) = (22) + (18) (this eliminates the x variable)
5y = 40 (collect terms)
y = 40/5 = 8 (divide both sides by 5)
x + 2(8) = 22 (substitute 8 for y in the first equation)
x = 22 - 16 = 6 (subtract 16 from both sides)
(x, y) = (6, 8)
2. Solve the first equation for n.
n = 74 - 9m (subtract 9m from both sides)
Substitute this into the second equation.
m - 8(74-9m) = 65
m - 8*74 + 72m = 65 (apply the distributive property)
73m = 65 + 592 (add 8*74 to both sides)
m = 657/73 = 9 (divide both sides by 73)
Substitute this answer back into our equation for n.
n = 74 - 9(9) = 74 - 81 = -7
(m, n) = (9, -7)
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