5. y = -4x, x - y = -10, (-2, 8)

Key takeaway: This question asks whether the ordered pair $(-2,8)$ is a solution of the given system. The key is to substitute the coordinates into both equations and verify whether each statement is true.

Step 1: Substitute the point into the first equation

Given $y=-4x$ and the point $(-2,8)$:

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

So the first equation is true.

Step 2: Substitute the point into the second equation

Given $x-y=-10$:

• $x-y=-2-8=-10$

So the second equation is also true.

Conclusion

Because the point $(-2,8)$ makes both equations true, it is a solution of the system.

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Pitfalls the pros know 👇 A common mistake is checking only one equation and stopping there. For a system, the point must satisfy every equation at the same time. Another error is sign handling, especially with $-4(-2)$ and $-2-8$.

What if the problem changes? If the ordered pair were different, the same method would still work: substitute the coordinates into each equation, then decide whether the pair is a solution, not a solution, or a solution only for one equation.

Tags: ordered pair, system of equations, substitution