Ineed to Write a system of EQUATIONS that has a solution of (5,2) , BUT it MUST be NON-LINEAR.
and then solve the system algebraically to verify that the solution is (5,2)
and then solve the system algebraically to verify that the solution is (5,2)
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Hello,
{ x = y + 3
{ y = √(x - 1) ←←← This is the non-linear equation
Solving by substitution:
y = √(x - 1)
y = √[(y + 3) - 1]
y = √(y + 2) ←←← This means y≥0
y² = y + 2 ←←← Squaring the equality
y² - y - 2 = 0
y² - 2y + y - 2 = 0
y(y - 2) + (y - 2) = 0
(y - 2)(y + 1) = 0
y=2 or y=-1
Since y≥0, y=2
Hence x=y+3=2+3=5
So the system has (x; y)=(5; 2) as solution.
Logically,
Dragon.Jade :-)
{ x = y + 3
{ y = √(x - 1) ←←← This is the non-linear equation
Solving by substitution:
y = √(x - 1)
y = √[(y + 3) - 1]
y = √(y + 2) ←←← This means y≥0
y² = y + 2 ←←← Squaring the equality
y² - y - 2 = 0
y² - 2y + y - 2 = 0
y(y - 2) + (y - 2) = 0
(y - 2)(y + 1) = 0
y=2 or y=-1
Since y≥0, y=2
Hence x=y+3=2+3=5
So the system has (x; y)=(5; 2) as solution.
Logically,
Dragon.Jade :-)
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42
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
life, the universe, and everything are based on math. the letters M,A,T,H and its corresponding numbers added up to 42. M A T H
13+1+20+8=42
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
life, the universe, and everything are based on math. the letters M,A,T,H and its corresponding numbers added up to 42. M A T H
13+1+20+8=42