Question

Solve the following system of2x + 6y = 14x – 6y= -20

Answer 1

We are given the following system of equations:

`\begin{gathered} 2x+6y=14,(1) \\ x-6y=-20,(2) \end{gathered}`

To solve the system we will use the method of elimination. We will add equations (1) and (2) so that the variable "y" gets canceled out, like this:

`2x+6y+x-6y=14-20`

Adding like terms:

`3x=-6`

Now, we divide both sides by 3:

`x=-(6)/(3)=-2`

Therefore, the value of "x" is -2. Now, we determine the value of "y" by substituting the value if "x" in equation (1):

`-2-6y=-20`

Now, we add 2 to both sides:

`\begin{gathered} -6y=-20+2 \\ -6y=18 \end{gathered}`

Now, we divide both sides by -6:

`y=(18)/(-6)=-3`

Therefore, the solution of the system is:

`\begin{gathered} x=-2 \\ y=-3 \end{gathered}`