Question

using the elimination method, what are the x and y (please explain I am very confused) :x + 3y =02x-3y=9

Answer 1

In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

Here, the given expressions are,

`\begin{gathered} x+3y=0\ldots\text{ (1)} \\ 2x-3y=9\ldots\text{.}(2) \end{gathered}`

From the equations 1 and 2 we can see that the coeffeicient of y is same, which is 3 and is of opposite sign. Therefore adding these equation, we get,

`\begin{gathered} x+3y+2x-3y=0+9 \\ 3x=9 \\ x=(9)/(3)=3 \end{gathered}`

Thus, we have the value of x, Now, substituting this value in the first equation, we get,

`\begin{gathered} 3+3y=0 \\ 3y=-3 \\ y=-(3)/(3)=-1 \end{gathered}`

Thus, the value of y is -1.