SOLUTION
Let us solve the simultaneous equation
[tex]\begin{gathered} -2x-y=0 \\ x-y=3 \end{gathered}[/tex]using elimination
To eliminate, we must decide which of the variables, x or y is easier to eliminate. The variable you must eliminate must be the same and have different sign. Looking above, it is easier to eliminate y because we have 1y above and 1y below. But to eliminate the y's, one must be +y and the other -y. So that +y -y becomes zero.
So to make the y's different, I will multiply the second equation by a -1. This becomes
[tex]\begin{gathered} -2x-y=0 \\ (-1)x-y=3 \\ -2x-y=0 \\ -x+y=-3 \end{gathered}[/tex]So, now we can eliminate y, doing this we have
[tex]\begin{gathered} -2x-x=-3x \\ -y+y=0 \\ 0-3=-3 \\ \text{This becomes } \\ -3x=-3 \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex]Now, to get y, we put x = 1 into any of the equations, Using equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2(1)-y=0 \\ -2-y=0 \\ \text{moving -y to the other side } \\ y=-2 \end{gathered}[/tex]So, x = 1 and y = -2
Using substitution, we make y or x the subject in any of the equations. Looking at this, It is easier to do this using equation 2. From equation 2,
[tex]\begin{gathered} x-y=3 \\ \text{making y the subject we have } \\ y=x-3 \end{gathered}[/tex]Now, we will put y = x - 3 into the other equation, which is equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2x-(x-3)=0 \\ -2x-x+3=0 \\ -2x-1x+3=0 \\ -3x+3=0 \\ -3x=-3 \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex]So, substituting x for 1 into equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2(1)-y=0 \\ -2\times1-y=0 \\ -2-y=0 \\ y=-2 \end{gathered}[/tex]Substituting x for 1 into equation 2, we have
[tex]\begin{gathered} x-y=3 \\ 1-y=3 \\ y=1-3 \\ y=-2 \end{gathered}[/tex]Now, for graphing,
