how many solution exist for each system of equations?

3x-3y=-6

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.

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