1. For example:
Could you tell that the equations y=2x +1 and y= 2x-7 have no solution?
Can you look at a system of linear equations and tell how many solutions it has?
For example:
Could you tell that the equation y=2x +1 and y= 2x-7 has no solution?

3. Slope intercept form of a line is y = mx +b where m is the slope and b is the y-int. The slope is the change in y over the change in x or rise over run. The y-int. is where the line crosses the y axis.

4. To graph the linear equation y = 2x + 1, determine the slope and y-int
To graph the linear equation y = 2x + 1, determine the slope and y-int. In this case, the slope is 2 and the y-int is 1.

5. To graph the linear equation y = 2x + 1, determine the slope and y-int
To graph the linear equation y = 2x + 1, determine the slope and y-int. In this case, the slope is 2 and the y-int is 1. Start at the point (0,1) and go up 2 and over 1.

7. There are three possibilities for the number of solutions for linear equations: one, none and infinitely many

8. y = 1 2 x - 5 y = 1 2 x - 3 One point one solution
Let’s look at three systems of linear equations. In the first set, they have different slopes. When they are graphed, they intersect in one point. This means that they system of equations has one solution.
In the second system of equations, the lines are parallel. They both have the same slope, but they have different y-int. These two lines do not share are common points, so they have no common solution.
The third system of equations is the same equation. When graphed, they are the same line, so they share infinitely many solutions.

9. Determine the number of solutions that the system has.
The system of equations is y = -4(x+4) and y = -4x-16. We need to have both equations in slope int. form. The first equation is not in the correct form, so we are going to distribute -4 across x+4. This gives us y = -4x-16. Both equations have the same slope and same y-int. This means that both equations are the same, so the system shares the same solution which is infinitely many solutions.

10. Slope: 1 2 , y-intercept: 1 y = 1 2 x + 1
Determine the number of solutions that the system has.
The system of equations is y = x+1 and y = 1/2x+1. First, we need to have both equations in slope int. form. They are, so now we need to determine the slope and y-int for both equations. The slope of y=x+1 is 1 and the y-int is 1. In the equation y =1/2x+1, the slope is ½ and the y-int is 1.
If you notice, the slopes are different. This tells us that the equation will intersect in one point. That means that the system of equations will have one solution.

11. Determine the number of solutions that the system has.
The system of equations is y = -5x + 1 and y = -5x-2. First, we need to have both equations in slope int. form. They are, so now we need to determine the slope and y-int for both equations. The slope of y=-5x+ 1 is -5 and the y-int is 1. In the equation y =-5x-2, the slope is -5 and the y-int is -2.
If you notice, the slopes are the same, but the y-int are different. This tells us that the lines are parallel which means that the system of equations will have no solutions because their graphs will never cross..

19. How many solutions does the system of equations have
How many solutions does the system of equations have? y=6(x+1) and y=6x+6
a) One b) None c) Infinitely Many
How many solutions does the system of equations have? y=-3x and y=x+1
a) One b) None c) Infinitely Many