Question

Use elimination to solve for x and y:9x - 4y = 11x + 4y = 19a) (3, 4)b) (4, 3)c) (7, 3)d) (-1, 5)

Answer 1

Given the following System of Equations:

$\begin{cases}9x-4y=11 \\ x+4y=19\end{cases}$

You can solve it using the Elimination Method:

1. Since the y-terms are:

$\begin{gathered} -4y \\ 4y \end{gathered}$

You can add the equations:

$\begin{gathered} \begin{cases}9x-4y=11 \\ x+4y=19\end{cases} \\ --------- \\ 10x+0=30 \\ 10x=30 \end{gathered}$

2. Now you need to solve for "x":

$\begin{gathered} x=\frac{30}{10} \\ \\ x=3 \end{gathered}$

3. Substitute the value of "x" into one of the original equations:

$\begin{gathered} x+4y=19 \\ (3)+4y=19 \end{gathered}$

4. Solve for "y":

$\begin{gathered} 3+4y=19 \\ 4y=19-3 \\ 4y=16 \\ \\ y=\frac{16}{4} \\ \\ y=4 \end{gathered}$

Therefore, you can write the solution in this form:

$(3,4)$

Hence, the answer is: Option a.