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The system has infinitely many solutions.
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The Deep Dive
Let’s have some fun solving this system of equations!
First, we can simplify the equations a bit. The first equation
can be simplified by dividing everything by 6, giving us
. Now, substitute
into the second equation
. Replacing
, we have:
Now, combine like terms:
This simplifies to
, which means the equations represent the same line, indicating an infinite number of solutions! So any point of the form
is a solution to this system.
For those learning to solve linear equations, remembering that two equations could represent the same line is a key concept!