To solve the two equations simultaneously using the substitution method we need to rearrange one of the equation to make either [tex]'x'[/tex] or [tex]'y'[/tex] the subject.
We can try in turn rearranging both equations and see which unknown term would have been easier to solve first
Equation [tex]2x+8y=12[/tex]
Making [tex]'x'[/tex] the subject
[tex]2x=12-8y[/tex] , dividing each term by 2
[tex]x=6-4y[/tex]⇒ (Option 1)
Making [tex]'y'[/tex] the subject
[tex]8y=12-2x[/tex], multiply each term by 8 gives
[tex]y= \frac{12}{8} - \frac{2}{8}x [/tex]⇒ (Option 2)
Equation [tex]3x-8y=11[/tex]
Making [tex]'x'[/tex] the subject
[tex]3x=11+8y[/tex], divide each term by 3
[tex]x= \frac{11}{3}+ \frac{8}{3}y [/tex] ⇒ (Option 3)
Making [tex]'y'[/tex] the subject
[tex]8y=3x-11[/tex], divide each term by 8
[tex]y= \frac{3}{8}x- \frac{11}{8} [/tex] ⇒ (Option 4)
From all the possibilities of rearranged term, the most efficient option would have been the first option, from equation [tex]2x+8y=12[/tex] with [tex]'x'[/tex] as the subject, [tex]x=6-4y[/tex]
