Question

How do you solve the following system of equations?: `x+y= -2 , x-2y=13`?

Answer 1

`x = 3`
`y = -5`

Explanation:

since we have two unknowns we need minimum of two equations to solve for them , and we have that too

lets see the first equation
`x+y =-2`
the first objective is to write either x in terms of y or y in terms of x
so i add -y to both sides , and we get
`x = -2-y`
take this value of x and plug it in equation 2
so
this `x-2y=13`
becomes
`(-2-y)-2y =13`
solve for y to get a value
`-2 -3y = 13`
`-3y = 15`
`-y = 5`
or
`y = -5`
since we got y value , we can plug it back in the first equation to get x value
`x + (-5) = -2` or `x = 5-2 = 3`
So , `x=3 , y=-5`

Answer 2

`x = 3`
`y = -5`

Explanation:

You add/subtract the two equations with each other, using the `=` sign as a point of reference:

`x+y = -2`

would be the first equation. We can label it as equation `(1)`

`x-2y = 13`

would be the second equation. We can label it as equation `(2)`

Now, we can subtract equation `(2)` from equation `(1)` [the idea here is to leave us with only one variable, that way we can solve the equation as usual]

`(1) - (2)` would be

`x-x + y-(-2y) = -2-13`

`0 + 3y = -15`

so

`y = -5`

Now we can take `y` and use it in equation `(1)`;

`x+(-5) = -2`

`x = 3`

So

`x = 3 and y = -5`