6. y = 2x + 6, x + 2y = -8, (-4, -2)

Expert intro: To test whether $(-4,-2)$ is a solution, substitute $x=-4$ and $y=-2$ into both equations. The point works only if both equations are true simultaneously.

Detailed walkthrough

Step 1: Check the first equation

For $y=2x+6$ and $(-4,-2)$:

• Right side: $2(-4)+6=-8+6=-2$
• Left side: $y=-2$

So the first equation is true.

Step 2: Check the second equation

For $x+2y=-8$:

• $x+2y=-4+2(-2)=-4-4=-8$

So the second equation is true.

Conclusion

The point $(-4,-2)$ satisfies both equations, so it is a solution of the system.

💡 Pitfall guide

Do not mix up the coordinates or forget that $2y$ means $2\times y$. A frequent mistake is to stop after the first equation even though a system requires both equations to be satisfied.

🔄 Real-world variant

If one coordinate changed, you would still use substitution first. For example, to test $(a,b)$ in this same system, check whether $b=2a+6$ and $a+2b=-8$ both hold.

🔍 Related terms

substitution, ordered pair, solution of a system