Question

What is the solution of the system. Use the substution method. 3x+2y=11, x-2=-4y

Answer 1

`x=(10)/(3)` and
`y=(1)/(2)`

Explanation:

• To use the substitution method, we should take one of the equations, and obtain an expression for one of the variables from this equation. Let's take the first one: 3x-2y = 11. We obtain an expression for x (it could be for y as well): 3x = 11 + 2 y ⇒
  `x=(11)/(3)+(2)/(3) *{y}`.
• Now, we should replace the expression obtain for x in the first equation, on the second equation, as follow

• 
  `x-2=4y`⇒
  `((11)/(3)+(2)/(3)*{y})-2=4*{y}`
• Then rearranging terms
  `(11)/(3)-2=4*{y}-(2)/(3)*{y}`
• This expression results in
  `y=(1)/(2)`
• Finally, using the firs equation, in which we obtained an expression from x,
  `x=(11)/(3)-(2)/(3) *{y}`, we replace y=1/2 and get
  `x=(11)/(3)- (2)/(3)*{(1)/(2) }`, then
  `x=(10)/(3)`