Given:
-x+3y=-9.........................................(1)
5x-2y=35..............................................(2)
color(red)("~~~~~~~~~~~~~~~~~~ All calculation shown ~~~~~~~~~~~~~~~")
For equation (1): making y the dependant variable (y=..)
Add color(blue)(x) to both sides so that it is removed from the left.
(3y-x) color(blue)(+x)=(-9)color(blue)(+x)
color(brown)("The brackets serve no purpose other than to show what")
color(brown)("is being altered or to group things so that they are obvious.")
3y=x-9
Divide both sides by 3
3/(color(blue)(3)) times y= x/(color(blue)(3)) -9/(color(blue)(3))
color(green)(y= 1/3 x-3......................................(1_a))
color(red)("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")
For equation (2): making y the dependant variable (y=..)
By sight!
color(green)(y= 5/2x-35/2...................................................(2_a))
color(red)("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")
Both equation (1_a) and (2_a) have a common value in y so
adopting "Equation "(1_a) =y = "Equation "(2_a) to solve for x
color(blue)(1/2x -3 )color(brown)(= y =) color(blue)(5/2x-35/2)
Giving:
color(blue)(1/2x -3 )color(brown)(=)color(blue)(5/2x-35/2)
Collecting like terms:
5/2x -1/2x =35/2-3
2x=29/2
Divide both sides by 2 giving
(2x) divide 2 =(29/2) divide 2
2/2x = 29/2 times 1/2
color(green)(x= 29/4............................................(3))
color(red)("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")
Now substitute for x using equation (3) into either equation (1_a) " or " (2_a) to determine the value of y.
I will let you do that!
