3b. If the y-intercepts are different, the two equations are distinct parallel lines and have NO SOLUTION. 3c. If the slopes are different, there will be ONE UNIQUE SOLUTION.

How many solutions does different slope and different y-intercept have?

3b. If the y-intercepts are different, the two equations are distinct parallel lines and have NO SOLUTION. 3c. If the slopes are different, there will be ONE UNIQUE SOLUTION.

What happens if two lines have the same y-intercept but different slopes?

If two lines have different slopes, they cannot be the same line. However, if they share a y-intercept, that means they cross the y -axis at the same y value. Since the x value is constant on the y-axis (0), they also share an x-value here.

What kind of solution will I have if I have same slopes but different y-intercepts?

If linear equations In x and y have the same slope but different y intercepts then the lines are parallel, and you have no solutions at all. If the lines have the same slope and the same y interecept, then they are exact same line and thus an infinite number of solutions.

How many solutions does a system of equations have if they both have the same slope but different y-intercepts resulting in parallel lines?

When lines have the same slope and different y-intercepts they are parallel lines. Parallel lines never intercept. Because these lines never intercept, they have no solution. Since they have no solution they are not consistent, dependent or independent like the last two systems we looked at.

When looking at the equations of a system of equations and the slopes are different What is the solution to that system of equations?

If the two lines have two different slopes, then they will intersect once. Therefore, the system of equations has exactly one solution. If the two lines have the same slope but different y-intercepts, then they are parallel lines, and they will never intersect.

When two linear equations are solved for Y and the slopes are different and the y-intercepts are equal the lines are?

If the two linear equations have the same slope (and different y-intercepts), the lines will be parallel. Since parallel lines never intersect, a system composed of two parallel lines will have NO solution (no intersection of the lines.)

Which kind of system of linear equations has lines with only different slopes?

A consistent system is considered to be an independent system if it has a single solution, such as the example we just explored. The two lines have different slopes and intersect at one point in the plane.

Do no solution equations have the same slope?

A system of linear equations has no solution if the lines have the same slope but different y-intercepts.

How will you compare the slope and y-intercept of each system?

In the equation of a straight line (when the equation is written as “y = mx + b”), the slope is the number “m” that is multiplied on the x, and “b” is the y-intercept (that is, the point where the line crosses the vertical y-axis).

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Can the slope and y-intercept be the same?

Summary. The slope-intercept form of a line is: y=mx+b where m is the slope and b is the y-intercept. The y-intercept is always where the line intersects the y-axis, and will always appear as (0,b) in coordinate form.

Can 2 different linear functions have the same y-intercept?

Yes, two different linear functions can have the same y-intercept. To illustrate this, consider the following two linear functions: y = 2x + 5. y = 8…

Will two lines having different slopes intersect coincide or be parallel?

If you have different slopes at one point the lines will cross each other since they are not parallel. Afterwards they will continue indefinitely onward in either direction, forever not crossing again. For two lines to be parallel they have to have the same slope.

What happens when two equations are the same?

Systems of equations that have the same solution are called equivalent systems. … Given a system of two equations, we can produce an equivalent system by replacing one equation by the sum of the two equations, or by replacing an equation by a multiple of itself.

Which systems of equations have no solution?

An inconsistent system has no solution. Notice that the two lines are parallel and will never intersect.

Which system of equation has no solution?

If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

What is the relationship between the slope and the y-intercept to the systems of linear equations?

Slope and y-Intercept Values The slope indicates the rate of change in y per unit change in x. The y-intercept indicates the y-value when the x-value is 0.

What kind of graph describes the system of linear equation with the same slope and the same y-intercept?

Linear systems composed of lines that have the same slope and the y-intercept are said to be consistent dependent systems.

What are the three different types of systems of linear equations in two variables?

• An independent system has exactly one solution pair (x,y) . The point where the two lines intersect is the only solution.
• An inconsistent system has no solution. …
• A dependent system has infinitely many solutions.

Which graph most likely shows a system of equations with no solutions ?'?

The graph of a system with one solution is two intersecting lines. The graph of system with no solutions is two parallel lines.

Do parallel lines have the same slope?

As mentioned above, parallel lines have the same slope. So, if we know the slope of the line parallel to our line, we have it made.

What kind of lines make up the graph of an inconsistent system of linear equation in two variables?

Another type of system of linear equations is an inconsistent system, which is one in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no points common to both lines; hence, there is no solution to the system.

When you graph the exact same equation twice?

If a system of linear equations has infinitely many solutions, what does this mean about the two lines? When you graph the exact same equation twice, you will have infinite solutions.

How can a system of equations have infinite solutions?

The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.

How do you interpret the slope and y-intercept of a regression line?

The greater the magnitude of the slope, the steeper the line and the greater the rate of change. By examining the equation of a line, you quickly can discern its slope and y-intercept (where the line crosses the y-axis). The slope is positive 5. When x increases by 1, y increases by 5.

Which two lines have the same Y intercept?

As can be seen on the graph ,there is only one point of intersection at y- intercept. If both the lines are parallel to the y- axis, then they will have the same y intercept. This is valid for any two parallel points in the lines.

What is same slope?

Parallel lines have the same slope.

Why does the graph of the new equation intersect the other two graphs at the same point?

A system of linear equations includes two or more linear equations. The graphs of two lines will intersect at a single point if they are not parallel. Two parallel lines can also intersect if they are coincident, which means they are the same line and they intersect at every point.

When both equations create the same line how many solutions are there?

Infinite Solutions If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. When the lines intersect, the point of intersection is the only point that the two graphs have in common.

Can equations that appear to be different be equivalent?

If “x” is the same for both equations, then they are equivalent. If “x” is different (i.e., the equations have different roots), then the equations are not equivalent.

What is known as simultaneous equations explain the different methods of solving simultaneous equations?

If you have two different equations with the same two unknowns in each, you can solve for both unknowns. There are three common methods for solving: addition/subtraction, substitution, and graphing.