Question

Determine the number of solutions the following systems of equations have without solving them algebraically and explain your reasoning.

a. 2x + 3y = 6
4x + 6y = 12

How many solutions does the system of linear equations have?


Explain your reasoning.

b. y=1/5x +2
y=1/5x +10

How many solutions does the system of linear equations have?


Explain your reasoning.

Answer 1

a. will have no solutions because the lines have the same slope, lines with the same slope will never intersect. b. will also have no solutions because the slopes of the two lines are the same as well, lines with equal slopes will not intersect, therefore will have no solution.