Question

Solve using elimination.
–6x + 3y = 3
–6x + 6y =18

Answer 1

Given:-

• 
  `\textsf{–6x + 3y = 3 --- eqⁿ ( i )}`

`\:`

• 
  `\textsf{–6x + 6y =18 --- eqⁿ ( ii )}`

`\:`

Now , subtract the eqⁿ ( i ) to eqⁿ ( ii ) :

`\sf{ \cancel{–6x} + 3y = 3} \\ \: \: \sf{ \cancel{–6x }+ 6y =18} \\ \sf{———————} \\ \: \: \: \: \: \: \: \: \: \: \: \: \textsf{ -3y = -15} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{y = \cancel( - 15)/( - 3) } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{ \purple{\textsf{ \: y = 5 \: }}}}`

`\:`

now , put the value of y = 5 in eqⁿ ( i ) :

• 
  `\textsf{–6x + 3y = 3}`

`\:`

• 
  `\textsf{–6x + 3( 5 ) = 3 }`

`\:`

• 
  `\textsf{–6x + 15 = 3}`

`\:`

• 
  `\textsf{–6x = 3 - 15}`

`\:`

• 
  `\textsf{–6x = - 12}`

`\:`

• 
  `\sf{x = \cancel( - 12)/( - 6)}`

`\:`

• 
  `\underline{ \boxed{\color{purple}{\textsf{ x= 2}}}}`

`\:`

`\green{ \boxed{ ( \boxed{ \sf \red{x = 2}} ,\boxed{ \sf \red{y = 5}} )}}`

`\:`

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps ⸙