Question

12x+10y=2

-x+4y= -5

Without actually solving, explain whether substitution or elimination would be a better method for solving the system.

Answer 1

Elimination would be a better method for solving the system.

Given equation

• 
  `\sf12x+10y=2`
• 
  `\sf-x+4y= -5`

Solution :-

`\Rrightarrow \sf12x+10y=2`

`\Rrightarrow \sf6x+5y=1.......(i)`

`\sf\Rrightarrow-x+4y= -5 ............(ii)`

`\large \sf \red{ \blue{[ (ii)×6]}}`

`\sf\Rrightarrow-6x+24y= -30 ............(iii)`

`\large \sf \red{(i) + \blue{ (iii)}}`

`\Rrightarrow \small\sf6x+5y=1+(-6x+24y= -30)`

`\Rrightarrow \sf29y = - 29 \\`

`\Rrightarrow \blue{\sf \: y = - 1}`

putting the value in equation (i)

`\Rrightarrow \sf6x+5 * - 1=1`

`\Rrightarrow \sf6x - 5=1`

`\Rrightarrow \sf6x = 6`

`\Rrightarrow \red{\sf \: x = 1}`

`\overline{\underline{\rule{209pt}{2pt}}}`