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What is the solution to the system of equations below? y = -2x - 6 and 2y = -4x - 12

no solution
infinitely many solutions
(–3, 0)
(3, –12)

Respuesta :

Answer: Infinitely Many Solutions

Step-by-step explanation:

Substitute y into the second equation:

2(-2x-6)=-4x-12

Then you get -4x-12=-4x=-12. Since this is 0=0 it would make it infinitely many solutions.

There are infinitely many solutions to the given system. The equations in the system are y = -2x - 6 and 2y = -4x - 12.

What are the solutions to a system?

For a system of linear equations, there are three types of solutions. They are,

  • Unique solution
  • No solution
  • Infinitely many solutions

Infinitely many solutions are there for a system if they both are equal on both sides while solving. (their graphs intersect at all the points)

Finding the solutions for the given system:

Given the system of equations as

y = -2x - 6

2y = -4x - 12

Using substitution method, substituting first equation into the second equation,

2( -2x -6) = -4x - 12

⇒ -4x -12 = -4x - 12

Thus, both sides are equal, and the given system has infinitely many solutions.

Learn more about solutions of a system here:

https://brainly.com/question/20430876

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