ANSWER:
(3, -6)
STEP-BY-STEP EXPLANATION:
We have the following system of equations:
[tex]\begin{gathered} 4x+y=6 \\ -5x-2y=-3 \end{gathered}[/tex]
We must solve by the elimination method, to do this we must multiply the first equation by 2 and then add both equations, to eliminate the variable y, just like this:
[tex]\begin{gathered} 2\cdot(4x+y=6)\rightarrow8x+2y=12 \\ \text{ Therefore:} \\ 8x+2y-5x-2y=12-3 \\ 3x=9 \\ x=\frac{9}{3} \\ x=3 \end{gathered}[/tex]
Knowing the value of x, we can calculate the value of y, substituting in the first equation:
[tex]\begin{gathered} 4\cdot3+y=6 \\ y=6-12 \\ y=-6 \end{gathered}[/tex]
Therefore, the solution of the system is (3, -6)
