Question

How do you solve the following linear system: `-9x - 5y = -1, 3x + y = 1`?

Answer 1

There are two methods: Substitution and addition, subtraction.
For this problem addition or subtraction would be the preferred method.
`x = 2/3 and y = -1`

Explanation:

Multiplying the second equation by 3 makes adding the two equations easy

`3 xx ( 3x + y = +1)` gives

`9x + 3y = +3`

Now add the two equations

`-9x - 5y = - 1`
`ul(+9x +3y = +3)`
`" "0x - 2y = +2` This is what it gives

Now solve for y by dividing both sides by `-2`

`( -2 y)/( -2) = (+2)/(-2)`

This gives `y = -1`

Put `- 1` into either equation for `y` and solve for `x`

`3x -1 = + 1 " "` Add + 1 to both sides of the equation

`3x - 1 +1 = +1 + 1`

This gives

`3x = 2" "` Divide both sides by 3

`(3x)/ 3 = (+2)/3" "` This gives

`x = 2/3`

The point of intersection is `(2/3, -1 )`

The substitution method would also work but in this case would be more difficult. An alternative would be to graph both equations and then find the point of intersection.