Question

Is the point `(2, -2)` a solution for the equations `3x + y = 4` and `x + 3y = -4`?

Answer 1

See a solution process below:

Explanation:

Equation 1:

Substitute `color(red)(2)` for `color(red)(x)` and substitute `color(blue)(-2)` for `color(blue)(y)` in the first equation and determine if the equation is true:

`3color(red)(x) + color(blue)(y) = 4` becomes:

`(3 xx color(red)(2)) + color(blue)((-2)) = 4`

`6 - 2 = 4`

`4 = 4`

Because this equation is true we can move to the next equation.

Equation 2:

Again, Substitute `color(red)(2)` for `color(red)(x)` and substitute `color(blue)(-2)` for `color(blue)(y)` this time in the second equation and determine if the equation is true:

`color(red)(x) + 3color(blue)(y) = -4` becomes:

`color(red)(2) + (3 xx color(blue)(-2)) = -4`

`color(red)(2) + (-6) = -4`

`color(red)(2) - 6 = -4`

`-4 = -4`

Because the first and second equation are both true for the point in the problem the point or ordered pair IS a solution for the system of equations.