4. \\begin{cases} 5x + 2y = 4 \\\\ 9x + 2y = 12 \\end{cases}

Explanation:

Step1: Subtract the two equations

We have the system of equations: $$\begin{cases}5x + 2y = 4\9x + 2y = 12\end{cases}$$ Subtract the first equation from the second equation: $$(9x + 2y)-(5x + 2y)=12 - 4$$ Simplify the left - hand side: $9x+2y - 5x - 2y=4x$, and the right - hand side: $12 - 4 = 8$. So we get $4x=8$.

Step2: Solve for x

Divide both sides of the equation $4x = 8$ by 4: $$x=\frac{8}{4}=2$$

Step3: Substitute x into one of the original equations

Substitute $x = 2$ into the first equation $5x+2y = 4$: $$5\times2+2y=4$$ Simplify the left - hand side: $10 + 2y=4$. Subtract 10 from both sides: $2y=4 - 10=-6$. Divide both sides by 2: $y=\frac{-6}{2}=-3$

Answer:

The solution of the system of equations is $x = 2,y=-3$