Anthony has rules for 3 lines : A, B, C

Question

when he solves a system for lines A & B, he gets no solution. 

When he solves a systemfor lines B & C, he gets infinite solutions. 

What solution will he get when he solves a system for lines A & C? 

 

need to show work with equations and tables. 

Answer 1

If lines A and B have no solutions, then the two are parallel, e.g. the same slope and thus never meet. A ≠ B

If lines B and C have infinite solutions, then one essentially lays on top of the other and count as the same line, thus B = C.

If A ≠ B and B = C, then A ≠ C, or no solutions.

 

You can make the equations based on the slope-intercept form

(y = mx + b), and when you make the equations for lines A and B, you give them the same slope, just change the b.

Line C will have the same equation for b, but if you want to mix it up a little, you can put it into point-slope format instead.

 

You can Make a table just by putting in values for x, and then the outputs for the line-points for A, B, and C:

X |     Y

   |A | B | C

---------------