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hackermcpe
The solution to the system is (2,-1) 
To make sure plug in the ordered pair into the system of equations

-2(2) - 3(-1) = -1
-4 - (-3) = -1
-1 = -1

3(2) + 6(-1) = 0
6 + -6 = 0
0 = 0
This ordered pair works and is your answer
(2,-1)

There are 2 types of systems of equations. The solution of the given system of equations is (2,-1).

What is a system of equations?

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.

The equations given are:

  • –2x – 3y = –1
  • 3x + 6y = 0

Let's write the first equation in terms of x,

[tex]-2x-3y = -1\\-2x=-1+3y\\x = \dfrac{-1+3y}{-2}[/tex]

Substitute the value of x in the second equation, we will get,

[tex]3x+6y=0\\\\3(\dfrac{-1+3y}{-2})+6y=0\\\\\dfrac{-3}{-2}+\dfrac{9y}{-2}+6y=0\\\\1.5-4.5y+6y=0\\\\1.5y = -1.5y\\\\y=-1[/tex]

Now, substitute the value of y in any one of the equations to get the value of x,

[tex]3x + 6y = 0\\\\3x + 6(-1) = 0\\\\3x-6=0\\\\3x=6\\\\x=2[/tex]

Hence, the solution of the given system of equations is (2,-1).

Learn more about the System of the equation:

https://brainly.com/question/12895249

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