Question

Solve the linear system. $$\begin{aligned}&3 x+y=12\\\&9 x-y=36\end{aligned}$$

Short answer

The solution to the system of equations is \(x=4\) and \(y=0\).

Step-by-step solution

Add the equations

Add the two equations together. That is, sum each side of the equation, respectively: \(3x+y+9x-y=12+36\). This will eliminate variable \(y\) from one equation.

Simplify

Simplify the resulted equation to find an equation with one variable only. Simplifying we get \(12x=48\).

Solve for x

Solve the equation \(12x=48\) to find the value of variable \(x\). Dividing both sides by 12 we get: \(x=4\).

Substitute x in one equation

In order to find the variable \(y\), substitute \(x=4\) in the first or in the second equation of the initial system. For instance, in the first one: \(3*4+y=12\).

Solve for y

Solving the equation \(3*4+y=12\) we obtain that \(y=0\).