Question

Solve the system of equations by substitution and determine whether the system is consistent, inconsistent, or dependent: -5x+y=-12 -10x+5y=-15 Please provide the solution and the conclusion regarding the consistency of the system.

Answer 1

To solve the system of equations by substitution, we solve one equation for one variable and substitute that expression into the other equation. The solution to the system of equations is x = -1.29 and y = -5.55. The system of equations is consistent because it has a unique solution.

Step-by-step explanation:

To solve the system of equations by substitution, we'll solve one equation for one variable and substitute that expression into the other equation. Let's start by solving the first equation for y:

y = -5x - 12

Now we substitute this expression for y in the second equation:

-10x + 5(-5x - 12) = -15

Simplifying the equation:

-10x - 25x - 60 = -15

-35x - 60 = -15

-35x = 45

x = -1.29

Now substitute this value of x back into the first equation to solve for y:

y = -5(-1.29) - 12

y = 6.45 - 12

y = -5.55

So the solution to the system of equations is x = -1.29 and y = -5.55.