Question

How do you solve the system of equations `6x - 3y = - 12` and `- 2x + y = - 8`?

Answer 1

See a solution process below:

Explanation:

Multiply each side of the second equation by `color(red)(-3)` giving:

`color(red)(-3)(-2x + y) = color(red)(-3) xx -8`

`(color(red)(-3) xx -2x) + (color(red)(-3) xx y) = -24`

`6x + (-3y) = -24`

`6x - 3y = -24`

Because the left side of both equations are equal we should be able to equate the right side of each equation as well.

However, -12 definitely does not equal -24.

Therefore, there are no solutions for `x` Or, the solution is the null or empty set:

`x = {O/}`

This indicates the two lines represented by this equation are parallel and not the same line.

Answer 2

As can be seen, both the equations have same slope and hence

they are parallel. They never meet and hence no solution.

Explanation:

Standard form of equation with slope is

`y = mx + c`

`6x - 3y = -12` Dividing by 3 both sides,

`2x - y = -4`

`y = 2x + 4` Eqn (1)

Slope of the Eqn (1) `m_1 = 2`

Second equation

`-2x + y = -8`. Rearranging the terms,

`y = 2x - 8`. Eqn (2)

Slope of the Eqn (2) `m_2 = 2`

As can be seen, both the equations have same slope and hence

they are parallel. They never meet and hence no solution.