The first thing you need to do in linear equations is isolate the variable. Meaning that you need to get the numbers on one side, and the variable (X, Y, etc) on the other
1) For the first problem the variable "y" is a fraction. They way to get rid of this fraction is by multiplying both sides by the denominator (bottom number)
Equation:1/2Y=1
Step one-Multiply both sides by the denominator "2"
2 x 1/2Y= 1 x 2
2x1/2=1 1x2=2
Answer: Y=2
2)On this equation you have an X variable and a Y. Your goal is to find X&Y
Equation: 5x+6y=3x+2
Find X
To find X you must isolate it, meaning have X on one side and Y and number on the other.
5x+6y=3x+2
Step one-Move X to left side
5x+(-3x)+6y=3x+(-3x)+2
3x+6y=2
Step two-Move the Y variable to the right side
3x+6y+(-6y)=2+(-6y)
3x=2-6y
Step three-You must now isolate X by dividing by the variable's leading number "3"
(3x/3)=(2/3)+(-6y/3)
Answer: x=2/3-2y
Find Y
5x+6y=3x+2
Step one-Move Y to left side
5x+6y+(-5x)=3x+2+(-5x)
6y=2+(-2x)
Step two-You must now isolate Y by dividing by the variable's leading number "6"
(6y/6)=(2/6)+(-2x/6)
y=(2/6)+(-2/6)x
Step three-Reduce the fractions
Answer: Y=1/3-1/3x
3) On this equation you have an X variable and a Y. Your goal is to find X&Y
Find X: To find X you must isolate it, meaning have X on one side and Y and number on the other.
2+ 1/2x=y
Step one: Move the 2 from the left to the right
2+(-2)+1/2x=y+(-2)
1/2x=y-2
Step two: Multiply both sides of the equation by the Denominator "2"
2 x (1/2x)= (2 x y) - (2 x -2)
x=2y-(-4)
Answer: x=2y+4
Find Y
2+ 1/2x=y
Step One: Y is already by itself and has no leading number. Therefore
Answer: Y=1/2x + 2
If you have any math questions, feel free to PM me