Question

Solve using substitution


x = y +3
-3x + 3y = 6

Answer 1

`\large\bf{\underline{\underline{\mathfrak{Question}:}}}`

Solve using substitution

x = y +3,

-3x + 3y = 6

`\large\bf{\underline{\underline{\mathfrak{Solution}:}}}`

Given that,

`{\small{\rm{x=y+3}}}`

Equation:

`{\small{\rm{-3x + 3y = 6}}}`

So,

By substituting the value of 'x' that is 'y+3' in the given equation we get,

`:{\Longrightarrow{\small{\rm{-3(y+3) + 3y = 6}}}}`

`:{\Longrightarrow{\small{\rm{-3y-9+ 3y = 6}}}}`

`:{\Longrightarrow{\small{\rm{\cancel{-3y}-9\cancel{+3y} = 6}}}}`

`:{\Longrightarrow{\small{\rm{x = 6+9}}}}`

`:{\Longrightarrow{\small{\rm{x = 15}}}}`

`{\therefore{\small{\rm{Value\:of\:x = 15}}}}`

Now to find the value of 'y' use the value of 'x' in the given equation.

`:{\Longrightarrow{\small{\rm{-3(15) + 3y = 6}}}}`

`:{\Longrightarrow{\small{\rm{-45+ 3y = 6}}}}`

`:{\Longrightarrow{\small{\rm{3y = 6+45}}}}`

`:{\Longrightarrow{\small{\rm{3y = 51}}}}`

`:{\Longrightarrow{\small{\rm{y =(51)/(3)}}}}`

`:{\Longrightarrow{\small{\rm{y =17}}}}`

`{\therefore{\small{\rm{Value\:of\:y = 17}}}}`

For verification:

`:{\Longrightarrow{\small{\rm{-3(15) + 3(17) = 6}}}}`

`:{\Longrightarrow{\small{\rm{-45+ 51 = 6}}}}`

`:{\Longrightarrow{\small{\rm{6= 6}}}}`

`:{\Longrightarrow{\small{\rm{L.H.S= R.H.S}}}}`

Hence verified!