Solve the following simultaneous equations. x + 3y = 2 , 2x + 8y = 6
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We have to solve the following set of simultaneous equations:
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x + 3y = 2
x = 2 - 3y
plug it in as x into the other equation:
2(2 - 3y) + 8y = 6
4 - 6y + 8y = 6
bring like terms to the same side:
-6y + 8y = 6 - 4
combine:
2y = 2
divide by 2
y = 1x + 3(1) = 2
x + 3 = 2
subtract 3
x = 2 - 3
x = -1(-1 , 1)
x + 3y = 2
x = 2 - 3y
plug it in as x into the other equation:
2(2 - 3y) + 8y = 6
4 - 6y + 8y = 6
bring like terms to the same side:
-6y + 8y = 6 - 4
combine:
2y = 2
divide by 2
- y = 1
now plug that into any of the problems:
x + 3(1) = 2
x + 3 = 2
subtract 3
x = 2 - 3
- x = -1
(-1 , 1)
We'll solve the system using substitution method and we'll write x from the 1st equation, with respect to y:
x = 2 - 3y
We'll substitute x in the 2nd equation:
2(2 - 3y) + 8y = 6
We'll remove the brackets:
4 - 6y + 8y = 6
We'll combine like terms:
2y = 6 - 4
2y = 2
y = 1
We'll substitute y in the first equation:
x + 3 = 2
x = 2 - 3
x = -1
The solution of the system is represented by the pair (-1 ; 1).
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