# Y = 1 2 x y = 1 2 x - 1 What happens if we graph a system of equations and the lines are parallel?

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y = 1 2 x y = 1 2 x - 1 What happens if we graph a system of equations and the lines are parallel?

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.

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.

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.

To solve the system of equations – which means how many solutions do the two equations share? Remember, linear equations can have one solution, no solution, or infinitely many solutions. The first step to solving a system of equations is to make sure that the equations are in slope-intercept form. Looking at both equations, we can see that the first is in slope-intercept form (y=mx+b), but the second is not. We need to convert the second equation to slope-int form. To do that, we will solve for y. We will use the addition property of equality and add 4 to both sides. This gives us y = 2x +4. Determine the slope and y-int for each equation.

Determine the slope and y-int for each equation
Determine the slope and y-int for each equation. So for y = 2x, the slope is 2 and y-int is 0. In y=2x+4, the slope is 2 and the y-int is 4.

These two equations in The graphs do not intersect
These two equations in The graphs do not intersect. The lines are parallel. This means that the lines will not intersect and no point will be a solution for the system of equations. So the system has no solution.

y = 1 2 x y = 1 2 x - 1 To solve the system of equations – which means how many solutions do the two equations share? Remember, linear equations can have one solution, no solution, or infinitely many solutions. The first step to solving a system of equations is to make sure that the equations are in slope-intercept form. Looking at both equations, we can see that they are not in slope-intercept form (y=mx+b). We will need to put both of these equation in slope-int. for, so we are going to solve each equation for y. In the first equation, we will use the addition property of equality and add x to both sides of th equation. This gives us 2y = x. We need to use the division property of equality and divide each side by 2. This leaves us with y = 1/2x. In the second equation, we will use the addition property of equality and add x to both sides of the equation. This leaves us with 2y = -2 + x. We then must divide each side by 2. This gives us y = 1/2x - 1.

y = 1 2 x Slope: 1 2 , y-intercept: 0 y = 1 2 x - 1
Determine the slope and y-int for each equation. So for y = 1/2x, the slope is 1/2 and y-int is 0. In y=1/2x-1, the slope is 1/2 and the y-int is -1

y = 1 2 x y = 1 2 x - 1 The graphs do not intersect. The lines are parallel. This means that the lines will not intersect and no point will be a solution for the system of equations. So the system has no solution.

y = x y = x - 1 If the slopes are the same, but the y-intercept is different, the lines will be parallel, meaning they will never cross. If they never cross, there won't be any point they share, and therefore no solution to the system."

Find the solution for the system of linear equations y = 1 2 x – 1 and y = 1 2 x – 5 by graphing.

y = 1 2 x - 1 y = 1 2 x - 5

The solution for the system of linear equations y=2x+1 and y=2x-3 is?
a) (-1,1) b) (1,-1) c)(-1,-1) d) no solution The solution for the system of linear equations y=-x+6 and y=-x-2 is? a) (2,-4) b) (-2,4) c) (-2,-4) d) no solution

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