Question

How do you solve `x+y=3`; `x+2y=5`?

Answer 1

• We can solve for the values of x and y using the 'Elimination by Substitution' method.

• Let's number the equations first:
  `x+y=3` ------(1)
  `x+2y=5`------(2)

In (1), by transposing `y` to the other side, we get
`x= 3 - y`
Substituting this value of `x` in (2), we get
`(3-y)+2y = 5`
`3+y=5`
`y=5-3`
`y=2`
Here, we eliminated `x` by substituting its value in (2)

• We Substitute this value of `y` in (1) to get
  `x+2=3`
  `x=3-2`
  `x=1`

• The Solution for the equations (1) and (2) is:
  `x=1 , y=2`

• Once we arrive at a solution, it is a good idea to VERIFY our answer

Substituting `x=1 , y=2` in (1) we get
Left Hand Side: `x+y = 1+2 = 3`(Right Hand Side)

Substituting `x=1 , y=2` in (2) we get
Left Hand Side: `x+y = 1+(2*2) = 5`(Right Hand Side)

We have verified our answer, and we can be sure that it's correct.