Tell if the pairs of lines will have one, infinite, or no solutions. show your work! a.) y1 = 2x + 6 and y2 = 2x – 3 this equation is solutions because b.) y1 = 3x + 2x – 6 and y2 = 5x - 6 this equation has infinte solutions because they both have the same equation. i will give 99 points. and a brainest. for the most explained and smart answer.

A) y1 = 2x + 6 and y2 = 2x – 3 Slope of y1 = 2
Slope of y2 = 2
Therefore the two lines are parallel.
Now equate the two expressions of y to see if they equal.  If they are equal, then the two lines are parallel and coincident, infinite number of solution.
If they are not equal, then there is no solution.
y1=y2 =>  2x + 6 = 2x – 3 
Cancel 2x on each side, give 6=-3 which is impossible.  So the two lines are not coincident, hence NO solution.

b. y1 = 3x + 2x – 6 and y2 = 5x - 6
Simplify y1 to give
y1 = 5x – 6 and y2 = 5x - 6
Both y1 and y2 have a slope of 5, so y1 and y2 are parallel.
Now check if y1=y2 =>
 3x + 2x – 6 = 5x - 6
5x-6 = 5x -6
Since both sides are identical, so y1 and y2 are parallel AND coincident.  Therefore there is an infinite number of solution.  In fact, the solution set is (-∞, +∞).

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