Direction:
Arrange each equation for the indicated variable in terms of the other variable in the equation.
[tex] \displaystyle \textsf{Example:\ } 5x+y=-4;y [/tex]
[tex] \displaystyle \textsf{Solution:\ } y= -5x-4 [/tex]
Solution:
[tex] \displaystyle \textsf{1.\ } y=x + 3;\ x [/tex]
[tex] \displaystyle y = x + 3 [/tex]
[tex] \displaystyle y - x = x - x + 3 [/tex]
[tex] \displaystyle y - x = 3 [/tex]
[tex] \displaystyle y - x - y = 3 - y [/tex]
[tex]\displaystyle - x = 3 - y[/tex]
[tex]\displaystyle - x / -1 = 3 / -1 - y / -1[/tex]
[tex]\displaystyle x = -3 + y[/tex]
[tex]\displaystyle \boxed{ x = y - 3 }[/tex]
[tex] \displaystyle \textsf{2.\ } x+2y=4;\ x [/tex]
[tex] \displaystyle x+2y=4 [/tex]
[tex] \displaystyle x+2y-2y=4-2y [/tex]
[tex] \displaystyle x=4-2y [/tex]
[tex] \displaystyle \boxed{ x=-2y + 4} [/tex]
[tex] \displaystyle \textsf{3.\ } 5x-y+9=0;\ y [/tex]
[tex] \displaystyle 5x-y+9=0 [/tex]
[tex] \displaystyle 5x-y+9 - (5x + 9)=- (5x + 9) [/tex]
[tex]\displaystyle 5x-y+9 -5x - 9= -5x - 9[/tex]
[tex] \displaystyle -y = -5x - 9 [/tex]
[tex] \displaystyle -y/-1 = -5x/-1 - 9/-1 [/tex]
[tex]\displaystyle \boxed{ y = 5x + 9}[/tex]
[tex] \displaystyle \textsf{4.\ } 3x-2y=6;\ x [/tex]
[tex] \displaystyle 3x-2y=6 [/tex]
[tex] \displaystyle 3x-2y+2y=6+2y [/tex]
[tex] \displaystyle 3x=6+2y [/tex]
[tex] \displaystyle 3x/3=6/3+2y/3 [/tex]
[tex] \displaystyle x=2+2y/3 [/tex]
[tex] \displaystyle x=2y/3+2 [/tex]
[tex] \displaystyle \boxed{ x=\frac{2y}{3} + 2 } [/tex]
[tex]\displaystyle \textsf{5.\ } 6x-4y=12;\ x[/tex]
[tex] \displaystyle 6x-4y=12 [/tex]
[tex] \displaystyle 6x-4y+4y=12+4y [/tex]
[tex] \displaystyle 6x=12+4y [/tex]
[tex] \displaystyle 6x/6=12/6+4y/6 [/tex]
[tex] \displaystyle x=2+2y/3 [/tex]
[tex] \displaystyle x=2y/3+2 [/tex]
[tex]\displaystyle \boxed{ x=\frac{2y}{3} + 2}[/tex]
