Question

solve the following system of linear equations by addition. indicate whether the given system of linear equations is consistent, inconsistent, or dependent. if the system is consistent, find the solution. (\begin{cases}-4x + 2y=-12\\2x + 2y = 24end{cases}) answer 5 points selecting an option will enable input for any required text boxes. if the selected option does not have any associated text boxes, then no further input is required. consistent ( , ) inconsistent dependent

Explanation:

Step1: Multiply first - equation by 2

Multiply the equation \(2x + 2y=24\) by 2. We get \(4x + 4y = 48\).

Step2: Add the two equations

Add \(4x + 4y = 48\) and \(-4x+2y=-12\).
\((4x + 4y)+(-4x + 2y)=48+( - 12)\)
\(4x+4y - 4x + 2y=48 - 12\)
\(6y = 36\)

Step3: Solve for y

Divide both sides of \(6y = 36\) by 6. \(y=\frac{36}{6}=6\).

Step4: Substitute y into the first equation

Substitute \(y = 6\) into \(2x+2y = 24\).
\(2x+2\times6=24\)
\(2x+12 = 24\)
\(2x=24 - 12\)
\(2x = 12\)
\(x = 6\)
Since there is a unique solution \((x = 6,y = 6)\), the system is consistent.

Answer:

Consistent, (6,6)