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} -(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=-(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=(10)/(-2)=-5 \\ y=-5 \end{gathered}`

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