Elimination method requires us to eliminate one of the variables so as to work with one variable to resolve the problem.
[tex]\begin{gathered} 4x+3y=11\ldots eqn1 \\ 3x-2y=4\ldots eqn2 \end{gathered}[/tex]We multiply eqn1 by 2 and eqn2 by 3
[tex]\begin{gathered} 8x+6y=22\ldots eqn3 \\ 9x-6y=12\ldots eqn4 \end{gathered}[/tex]We then add eqns 3 and 4 to get:
[tex]17x=34\ldots eqn5[/tex]Now we have eliminated variable y, we can easily solve for x by dividing both sides of eqn 5 by 17
[tex]\begin{gathered} \frac{17x}{17}=\frac{34}{17} \\ x=2 \end{gathered}[/tex]The next step is to substitute this value of x into any of equations 1 - 4. We use eqn 1
[tex]\begin{gathered} 4(2)+3y=11 \\ 8+3y=11 \\ \text{Subtract 8 from both sides to get:} \\ 3y=11-8 \\ 3y=3 \\ \text{Divide both sides by 3 gives:} \\ y=1 \end{gathered}[/tex]The solution to our problem is (2, 1)
