what is the solution to this system of linear equations?\ny - x = 6\ny + x = -10\n(-2, -8)\n(-8, -2)\n(6…

Explanation:

Step1: Add the two equations

Add $y - x=6$ and $y + x=-10$: $$(y - x)+(y + x)=6+( - 10)$$ Simplify the left - hand side: $y - x+y + x = 2y$, and the right - hand side: $6+( - 10)=6 - 10=-4$. So, $2y=-4$.

Step2: Solve for $y$

Divide both sides of $2y=-4$ by 2: $y=\frac{-4}{2}=-2$

Step3: Substitute $y$ into the first equation

Substitute $y = - 2$ into $y - x=6$: $-2 - x=6$

Step4: Solve for $x$

Add 2 to both sides: $-x=6 + 2=8$, then multiply both sides by - 1 to get $x=-8$

Answer:

B. $(-8,-2)$