How many solutions exist for each system of equations?

1. \(3x - 3y = -6\)

2. \(y = x + 2\)

The second one is already in slope-intercept form. We need to do a little work on the first one.
3x - 3y = -6
Subtract 3x from each side:
-3y = -3x - 6
Divide each side by -3 :
y = x + 2
That's the first equation. But when you unravel it like this, you find that it's exactly the same as the second equation. Both of them represent the same straight line on a graph. If you graphed both of them, you'd only see one line !
The 'solution' of a pair of equations is the point on a graph where their lines cross. There's no such point here, because each and every point of the first equation is also a point of the second one.
This pair (system) of equations has no solution.

Answered by AL2006 | 2024-06-10

The system of equations consists of two identical equations, which means they represent the same line. Therefore, there are infinitely many solutions to this system of equations. Every point on the line y = x + 2 is a valid solution.
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Answered by AL2006 | 2024-12-23