# The graph of a system of equations will intersect at exactly 1 point.?

IS IT ALWAYS NEVER OR SOMETIMES

Generally. It is doable that it’s going to by no means occur (e.g., two parallel traces). It is also doable which you could get multiple intersection level (e.g., a line slicing a parabola).

Generally.
Take the case of two linear equations.
If the equations are of the identical line, there are an infinite variety of intersections.
If the equations are of parallel traces, there are not any intersections.
If the equations have totally different slopes, there shall be precisely one intersection.

there are three circumstances:

once they intersect at just one level.

once they by no means intersect i.e. are parallel.

once they utterly overlap (on this case there are infinite factors which might be widespread).

for case 1 the eq have just one answer.
ex: x+y=2;
2x+3y=6;
for case 2 the eq donot have any answer
x=2y;

x=2y+3;
for case 3 there are infinite solutions.
x=y+3;
2x-2y=12/2;

once they intersect at just one level.

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once they by no means intersect i.e. are parallel.