Question

Solve using elimination method2x+y=-2 -2x-3y=-6.

Answer 1

The system of equations we have is:

`\begin{gathered} 2x+y=-2 \\ -2x-3y=-6 \end{gathered}`

And we need to solve it using the elimination method.

Elimination method: consists of adding or subtracting the equations in the system such that one variable is eliminated.

In this case, we are going to add the two equations in the system in order to eliminate the variable x.

Adding the equations:

-Align the equation:

We start by adding 2x and -2x, which results in 0, so the x variable is eliminated.

Continue adding y and -3y:

`y+(-3y)=y-3y=-2y`

And now, we add the numbers to the right of the equal sign:

`-2+(-6)=-2-6=-8`

We get the blue equation:

`-2y=-8`

This is an equation that we can use to solve for y by dividing both sides by -2:

`\begin{gathered} y=(-8)/(-2) \\ y=4 \end{gathered}`

Once we have the value for one of the variables, we use it to find the value of the other variable.

In this case, we use the first equation of the system:

`2x+y=-2`

And substitute the value of y:

`y=4`
`2x+4=-2`

And solve for x.

The first step to solve for x is to subtract 4 to both sides:

`\begin{gathered} 2x=-2-4 \\ 2x=-6 \end{gathered}`

And then, divide both sides by 2:

`\begin{gathered} x=-(6)/(2) \\ x=-3 \end{gathered}`

Answer:

x=-3 and y=4