Question

Solve the simultaneous equation only by substitution method
3+x+x-y=0
2x+5y=8

Answer 1

Explanation:

to check your answers, substitute the x and y values into the given equations.

Answer 2

• 
  `{ \boxed{ \sf{x = ( - 7)/(12)}}}`

• 
  `{ \boxed{ \sf{y = (11)/(6)}}}`

Explanation:

Solve the simultaneous equation only by substitution method

`\sf 3 + x + x - y = 0 - - - (1)`

Solving for x,

`\sf 3 + 2x - y = 0`

`\sf 2x = y - 3`

`\sf{x = (y - 3)/(2)} - - - (2)`

`\sf 2x + 5y = 8`

`\sf 2x = 8 - 5y - - - - (3)`

Substitute equation 2 in equation 3.

`\sf 2 \bigg( (y - 3)/(2) \bigg) = 8 - 5y \\ \\ \sf (2y - 6)/(2) = 8 - 5y \\ \\ \sf 2(8 - 5y) = 2y - 6\\ \\ \sf16 - 10y = 2y - 6\\ \\ \sf16 + 6 = 2y + 10y\\ \\ \sf22 = 12y \\ \\ \sf y= (22)/(12) \\ \\ { \boxed{ \sf{y = (11)/(6)}}}`

Substitute value of y in the equation 3.

`\sf2x = 8 - 5y\\ \\ \sf2x = 8 - 5 \bigg( (11)/(6) \bigg) \\ \\ \sf2x = (8)/(1) - (55)/(6) \\ \\ \sf2x = (48 - 55)/(6) \\ \\ \sf2x = ( - 7)/(6) \\ \\ \sf x = ( - 7)/(2 * 6) \\ \\ { \boxed{ \sf{x = ( - 7)/(12)}}}`

`\rule{200}2`