Question

{{PLZ HELP}} Use algebraic rules of equations to predict the solution to the system of equations. Include all of your work for full credit.

{x+2y=10
{6y=-3x+30

Answer 1

Hello!

x+2y=10
x=10-2y

6y=-3(10-2y)+30
6y=-30+6y+30
0=0

Hope this Helps! :)

Answer 2

The system of equation has infinite number of solutions

Explanation:

The given system of equations is

`\left \{ {{x+2y=10} \atop {6y=-3x+30}} \right.`

First, we need to rewrite the system in order

`\left \{ {{x+2y=10} \atop {3x+6y=+30}} \right.`

Now, we multiply the first equation by -3, and solve

`\left \{ {{(-3)(x+2y)=(-3)(10)} \atop {3x+6y=+30}} \right.\\\\\left \{ {{-3x-6y=-30} \atop {3x+6y=+30}} \right.\\\\0x+0y=0`

This means the system of equation has infinite number of solutions, that is, it's a consistent system.

The reason of this result is because both equation represent the same line, it's like one line is on top of the other, sharing all points, that's why it has infinte solutions.