The system of equations below has exactly one (x, y) pair for its solution. 4x+6y=244x+6y=24
2x+y=82x+y=8
If we double each side of the second equation, 2x+y=82x+y=8, we have 4x+2y=164x+2y=16. Explain why the same pair that is the solution to the system is also a solution to this new equation.
If needed, you can support your explanation with hanger diagrams (upload a picture), or by inventing a situation that the equations represent.
If we add the two equations in the original system, we have 6x+7y=326x+7y=32. Explain why the same (x, y) pair is also a solution to this equation.
Again, you can support your explanation with diagrams or a situation, if needed.