Question

Solve the system of equations below using any method you learned in this unit. Show all work (even if you are using your calculator). elmianation method would be preferred but whatever works

Answer 1

Given

$\begin{gathered} 3x-4y=11...Equation\text{ i} \\ 2x+3y=-1...Equation\text{ ii} \end{gathered}$

Using Elimination method

Solution

Multiply the first equation by 3 and multiply the second equation by 4.

$\begin{gathered} 3\left(3x−4y=11\right) \\ 4\left(2x+3y=−1\right) \end{gathered}$

Becomes

$\begin{gathered} 9x−12y=33 \\ 8x+12y=−4 \end{gathered}$

Add these equations to eliminate y:

$17x=29$

Divide both sides by 17

$\begin{gathered} \frac{17x}{17}=\frac{29}{17} \\ \\ x=\frac{29}{17} \end{gathered}$

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

$\begin{gathered} 3x−4y=11 \\ \\ \\ Substitute\text{ x=}\frac{29}{17} \\ \\ 3(\frac{29}{17})-4y=11 \\ \\ \frac{87}{17}-4y=11 \\ \\ solve\text{ for y} \end{gathered}$$\begin{gathered} −4y=11-\frac{87}{17} \\ -4y=\frac{100}{17} \\ \\ divide\text{ both sides by} \\ y=-\frac{25}{17} \end{gathered}$

The final answer

$x=\frac{29}{17},\:y=-\frac{25}{17}$