How do you solve the system using the elimination method for \[-4x-2y=-12\] and \[4x+8y=-24\]?

Hint: For the given question we are given to solve the two equations i.e. \[-4x-2y=-12\] and \[4x+8y=-24\]by elimination method. For that we have to eliminate one of the variables to get solved. We have to multiply the first equation with ‘-sign’ and then we have to add both equations to get the solution.

Complete step by step solution:
For the given problem we are given to solve the system using elimination method for equations\[-4x-2y=-12\] and \[4x+8y=-24\]
Now let us consider the two equations as equation (1) and equation (2)
\[-4x-2y=-12............(1)\]
Second equation will be
\[4x+8y=-24............(2)\]
In the question it is given that we have to solve the problem using elimination methods. Which means you either add or subtract the equations to get an equation in one variable.
To get the equation in one variable we have to eliminate the other variable i.e. we have to make one of the variable’s coefficients should be in opposite in the two equations.
By observing the two equations we can say that the coefficient of x is same but with two different signs as ‘+sign’ and ‘-sign’
So we can add both the equations (1) and (2)
\[\Rightarrow -4x-2y+4x+8y=-12-24\]
By simplifying the above equation, we get
\[\Rightarrow 6y=-36\]
\[\Rightarrow y=\dfrac{-36}{6}\]
Let us consider the above equation as equation (3) and substitute in equation (1), we get
 \[\Rightarrow y=\dfrac{-36}{6}............(3)\]
\[\Rightarrow -4x-2\left( \dfrac{-36}{6} \right)=-12\]
 By simplifying the above equation, we get
\[\Rightarrow -4x-2\left( -6 \right)=-12\]
\[\Rightarrow -4x+12=-12\]
\[\Rightarrow -4x=-12-12\]
\[\Rightarrow -4x=-24\]
\[\Rightarrow 4x=24\]
\[\Rightarrow x=\dfrac{24}{4}\]
\[\Rightarrow x=6\]
Let us consider it as equation (4), we get
\[\Rightarrow x=6............\left( 4 \right)\]
Therefore, equation (3) and (4) are solutions for the given problem.

Note: We should note a point that if the problem is given to solve in elimination we should do the problem in elimination method only. We can eliminate any variable for solving this problem. Students should be careful while sign conversion.