Answer:
(-3, 4)
Step-by-step explanation:
We are solving the given system of equations by elimination:
[tex]\begin{cases}10x+6y=-6\\10x+8y=2\end{cases}[/tex]
This method entails subtracting one equation from the other.
In this case, we can subtract the first equation from the second equation:
[tex]\text{ }\ \ \,10x+8y=2\\\underline{-(10x+6y=-6)}[/tex]
[tex]0 + 2y = 2 - (-6)[/tex]
[tex]2y = 8[/tex]
[tex]\boxed{y=4}[/tex]
Now that we have solved for y, we can solve for x by substituting in the y-coordinate of the solution into one of the original equations:
[tex]10x+6(4) = -6[/tex]
[tex]10x+24=-6[/tex]
[tex]10x = -6 - 24[/tex]
[tex]10x = -30[/tex]
[tex]\boxed{x=-3}[/tex]
So, the solution to the system of equations is:
[tex]\huge\boxed{(-3,4)}[/tex]
