Question

Solve the system of equations by using elimination. Show all work for full credit. List your answer as an ordered pair.4x + 3y = 113x - 2y = 4

Answer 1

Elimination method requires us to eliminate one of the variables so as to work with one variable to resolve the problem.

`\begin{gathered} 4x+3y=11\ldots eqn1 \\ 3x-2y=4\ldots eqn2 \end{gathered}`

We multiply eqn1 by 2 and eqn2 by 3

`\begin{gathered} 8x+6y=22\ldots eqn3 \\ 9x-6y=12\ldots eqn4 \end{gathered}`

We then add eqns 3 and 4 to get:

`17x=34\ldots eqn5`

Now we have eliminated variable y, we can easily solve for x by dividing both sides of eqn 5 by 17

`\begin{gathered} (17x)/(17)=(34)/(17) \\ x=2 \end{gathered}`

The next step is to substitute this value of x into any of equations 1 - 4. We use eqn 1

`\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}`

The solution to our problem is (2, 1)