Question

How do you solve the following linear system: #3x + y = -6 , 3x + 2y = 9 #?

Answer 1

`color(green)(x = -7`
`color(green)( y = 15`

Explanation:

`3x + y = -6` --------(1)
`3x + 2y = 9` ------(2)

To solve the equation, we need to find the value of `x and y`

The fastest way to solve for the value of `y` would be by subtracting equation (1) from equation (2)

`(3x + 2y) - (3x+y) = 9 - (-6)`

`cancel(3x) - cancel(3x) + 2y - y = 9 + 6`

`color(green)( y = 15`

To get the value of `x`, we can substitute this value of `y` in any of the two equations

Substituting `y = 15` in the first equation, we get

`3x + 15 = -6`

Transposing 15 to the right side gives us

`3x = -6-15`

`3x = -21`

`x = -21/3`

`color(green)(x = -7`