Possible Solutions: No solution or infinitely many solutions Explanation: See solution.
Practice makes perfect
We are told that the lines described by the equations have the same slope in a system of linear equations. To find the possible solutions to the system, we will examine the positions of two lines with the same slope relative to each other. First, recall that a represents the slope and b represents the y-intercept in slope-intercept form.
y= ax+ bNow, take a closer look at the y-intercepts of the lines that have the same slope a.
From the graph we can observe two cases for the possible solutions of the system with two linear equations that have the same slope a.
Explanation
Generalization
Solution
Case I
The lines have the same slope but different y-intercepts.
y= ax+ m y= ax+ n m ≠ n
No solution
Case II
The lines have the same slope and y- intercept.
y= ax+ m y= ax+ n m = n
Infinitely many solutions
There are two possible solutions to a system with equations that have the same slope: no solution or infinitely many solutions.
