Question

X – 2y = -2 3x -6y = 30
Sloved by Elimination

Answer 1

No solutions.

Explanation:

When given the following system of equations,

`\left \{ {x-2y=-2} \atop {3x-6y=30}} \right.`

Solve by the process of elimination. The process of elimination is when one manipulates one or both of the equations such that one of the variables is the inverse of the other variable in its corresponding equation. When one adds the system, one of the variables will cancel, and one can solve for the other variable, then back solve for the canceled variable.

In this case, one can see that all terms in the second equation have a common factor of (3), to make manipulating the equation easier, divide the entire equation by (3).

`\left \{ {{x-2y=-2} \atop {3x-6y=30}} \right.`

`\left \{ {{x-2y=-2} \atop {x-2y=10}} \right.`

However, in doing so, one can see that the left sides of the equation are equal, however, the right side is not. Such a statement is not possible, thus there are no solutions to this system of equations.