Question

Solve the following system of equations What does x & y = ?

Answer 1

Given the system of equations, notice that we can divide by -2 the second equation to get the following equivalent equation:

$\begin{gathered} -\frac{1}{3}(3x+6y=-39) \\ \Rightarrow-x-2y=13 \end{gathered}$

then, we woul have the following equivalent system of equations:

$\begin{cases}4x+2y=-{22} \\ -x-2y=13\end{cases}$

if we add both equations, we can find the value of x:

$\begin{gathered} 4x+2y=-22 \\ -x-2y=13 \\ ---------- \\ 3x=-22+13=-9 \\ \Rightarrow x=-\frac{9}{3}=-3 \\ x=-3 \end{gathered}$

now that we know that x = -3, we can use this value to find the value of y:

$\begin{gathered} -(-3)-2y=13 \\ \Rightarrow-2y=13-3=10 \\ \Rightarrow y=\frac{10}{-2}=-5 \\ y=-5 \end{gathered}$

therefore, the solutions are x = -3 and y = -5