To go from the first red term 3x to the second red term 9x, we multiply by 3
The same can be said going from the first blue -y term to the second blue term -3y
So far, we have multiplied the left hand side (LHS) of the first equation by 3 to get the LHS of the second equation.
Therefore, to go from the first green term 10 to the second green term c, this means we also multiply by 3. This is to keep the equation balanced. So
If , then the system of equations would be
3x - y = 10
9x - 3y = 30
The second equation is the result of multiplying both sides by 3. Both equations will graph out the same line. In other words, one line is directly on top of the other so they intersect at an infinite number of points, which is why this system has infinitely many solutions.
Side note: if the value of c is not equal to 30, then we'll have two parallel lines, which in this case the inconsistent system has no solutions.
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