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. As we can see here the coefficient of x in both equations are equal but of opposite sign. So by doing addition we can eliminate ‘x’ and then by solving we will have our results.

Complete step by step answer:
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 method. 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 co-efficient should be in opposite in the two equations.
By observing the two equations we can say that the co-efficient 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: Here we can see that value of x and y are 6,-12 respectively. To know whether our answers are correct let us do verification by substituting values of x and y in equation (1) i.e. LHS of equation (1) will be
\[\begin{align}
  & \Rightarrow -4\left( 6 \right)-2\left( -6 \right) \\
 & \Rightarrow -24+12 \\
 & \Rightarrow -12 \\
\end{align}\]
The RHS of the equation (1) is -12. Therefore the values of ‘x’ and ‘y’ are correct.