Question

solve the following system of linear equations by substitution and determine whether the system is consistent, inconsistent, or dependent. if the system is consistent, find the solution.
{-5x - 8y = 11
-10x - 16y = 22
answer 5 points
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consistent
(

)
inconsistent
dependent

Explanation:

Step1: Manipulate the second - equation

Multiply the second equation \(-5x - 8y=11\) by 2. We get \(2(-5x - 8y)=2\times11\), which simplifies to \(-10x-16y = 22\), the same as the first equation.

Step2: Determine the nature of the system

Since the two equations are essentially the same, the system has infinitely many solutions. A system with infinitely many solutions is a dependent system.

Answer:

Dependent