Write out the two-equation given
[tex]\begin{gathered} 2x-y=7-----equation(1) \\ -2x+3y=9------\text{equation}(2) \end{gathered}[/tex]In other to use the elimination method, we ensure that one of the variables in the two-equation has the same coefficient.
By observation, it can be seen that the coefficient of the x in the two equations is the same. So we add two equations together because they have different signs to eliminate x
i.e.
[tex]\text{equation}(1)+\text{equation}(2)[/tex]Therefore,
[tex]\begin{gathered} 2x+(-2x)-y+(+3y)=7+9 \\ -y+3y=16 \\ 2y=16 \\ y=\frac{16}{2} \\ y=8 \end{gathered}[/tex]Substitute the value of y in any of the two equations to get the value of x. Let us pick equation(1)
[tex]\begin{gathered} 2x-y=7 \\ y=8 \\ 2x-8=7 \\ 2x=7+8 \\ 2x=15 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{15}{2} \\ x=7.5 \end{gathered}[/tex]Hence, x=7.5, y=8 (7.5,8)
