What is x and y when 3x+y=6 and y=x-2?

1 Answer
Dec 11, 2017

the point common to both plots is (x,y)->(2,0)

Explanation:

Given:

3x+y=6" ".....................Equation(1)
y=x-2" "......................Equation(2)

color(blue)("Determine the value of "x)

Using Eqn(2) substitute for color(red)(y) in Eqn(1) giving:

color(green)(3x+color(red)(y)color(white)("d")=color(white)("d")6 color(white)("dddd") ->color(white)("dddd")3x+(color(red)(x-2))color(white)("d")=color(white)("d")6)

color(green)(color(white)("ddddddddddd.d")->color(white)("dddddd") 4xcolor(white)("ddd")-2color(white)("ddd")=color(white)("d")6)

Add color(red)(2) to both sides

color(green)(4x-2color(white)("d")=color(white)("d")6 color(white)("dddd") ->color(white)("dddd")4xcolor(white)("d")-2color(red)(+2)color(white)("dd")=color(white)("d")6color(red)(+2))

color(green)(color(white)("ddddddddddddd.d")->color(white)("dddd") 4xcolor(white)("d")+color(white)("d")0color(white)("dddd")=color(white)("dd")8

Divide both sides by color(red)(4)

color(green)(4xcolor(white)("d")=color(white)("d")8color(white)("dddddd.d")->color(white)("dddd") 4/color(red)(4)xcolor(white)("d")=color(white)("d")8/color(red)(4) )

color(green)(color(white)("ddddddddddddd.d")->color(white)("dddddd") xcolor(white)("d")=color(white)("d")2 )
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

color(blue)("Determine the value of "y)

Substitute for color(red)(x=2) in Eqn(1)

color(green)(ycolor(white)("d")=color(white)("d")color(red)(x)-2 color(white)("dddd")->color(white)("dddd")ycolor(white)("d")=color(white)("d")color(red)(2)-2)

color(green)(color(white)("dddddddddddddd")->color(white)("dddd")ycolor(white)("d")=color(white)("d")0)

color(magenta)("So the point common to both plots is "(x,y)->(2,0))

Tony BTony B