Question

How do you solve this system of equations: `-3x - 3y = 0 and - 3x - 10y = 14`?

Answer 1

`x=2` and `y=-2`

Explanation:

As `-3x-3y=0`, `-3x=3y`

Putting this in `-3x-10y=14` we get

`3y-10y=14`

or `-7y=14`

or `y=14/(-7)=-2`

and `-3x=3×(-2)`

or `-3x=-6`

or `x=(-6)/(-3)=2`

Hence `x=2` and `y=-2`

Answer 2

x = 2 and y = -2

Explanation:

Given:

`-3x - 3y = 0 and -3x - 10y = 14`

Let `-3x = 3y`
Now, we substitute for `-3x` in `-3x - 10y = 14`, that is;

`3y - 10y = 14`
`-7y = 14`
`color(red)(y = -2)`

Next, substitute the value of y in any one of the above equations to get the respective x value;

`-3x - 10(-2) = 14`
`-3x + 20 = 14`
`-3x = -6`
`color(red)(x = 2)`

Therefore, `x = 2` and `y = -2.`

Answer 3

`x=2 and y=-2`

Explanation:

Note that the terms in `x` are the same in each equation.

Isolate the `x` term, make it the subject in each equation.

`-3x = 3y" "and" " -3x = 10y+14`

We know that `-3x =-3x`, so equating the right sides gives:

`10y +14 = 3y" "larr` now solve for `y`

`10y -3y = -14`

`7y = -14`

`y =-2`

Use the value of `y` to find `x`

`-3x = 3(-2)`

`-3x = -6`

`x =2`

Check in the second equation.

`-3x = 10y+14`

`-3(2)" "and" "10(-2)+14`

`-6" " and " "-20+14`

`-6=-6`