Solve the following simultaneous equations. 3x + 2y = 6, 18x + y = 9
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We have to solve the following set of simultaneous equations:
3x + 2y = 6 ...(1)
18x + y = 9 ...(2)
6*(1) - (2)
=> 18x + 12y - 18x - y = 36 - 9
=> 11y = 27
=> y = 27/11
substitute in (2)
18x + 27/11 = 9
=> 18x = 9 - 27/11
=> 18x = 72/11
=> x = 4/11
We get x = 4/11 and y = 27/11
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We'll solve the system using substitution, instead elimination.
We'll change the 2nd equation into:
y = 9 - 18x
3x + 2(9 - 18x) = 6
We'll remove the brackets:
3x + 18 - 36x = 6
We'll combine like terms:
-33x = 6-18
-33x = -12
We'll divide by -3:
11x = 4
x = 4/11
We'll substitute the value of x into:
y = 9 - 18x
y = 9 - 18*4/11
y = (99 - 72)/11
y = 27/11
The solution of the system is represented by (4/11 ; 27/11).
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