Is this true?If the graphs of two linear equations in a system have the same slope, the system always has no?

Answer 1

It is if they have the same slope that means they travel in to differnt lines that will never ever meet on the same plane therefore no solution

Answer 2

A linear system of two equations with two variables is any system that can be written in the form.



where any of the constants can be zero with the exception that each equation must have at least one variable in it.



Also, the system is called linear if the variables are only to the first power, are only in the numerator and there are no products of variables in any of the equations.



Here is an example of a system with numbers.








Before we discuss how to solve systems we should first talk about just what a solution to a system of equations is. A solution to a system of equations is a value of x and a value of y that, when substituted into the equations, satisfies both equations at the same time.



For the example above and is a solution to the system. This is easy enough to check.










So, sure enough that pair of numbers is a solution to the system. Do not worry about how we got these values. This will be the very first system that we solve when we get into examples.



Note that it is important that the pair of numbers satisfy both equations. For instance and will satisfy the first equation, but not the second and so isn’t a solution to the system. Likewise, and will satisfy the second equation but not the first and so can’t be a solution to the system.



Now, just what does a solution to a system of two equations represent? Well if you think about it both of the equations in the system are lines. So, let’s graph them and see what we get.


Example 1 Solve each of the following systems.

(a)



(b)

Solution

(a) So, this was the first system that we looked at. We already know the solutions, but this will give us a chance to verify the values that we wrote down for the solution.



Now, the method says that we need to solve one of the equations for one of the variables. Which equation we choose and which variable that we choose is up to you, but it’s usually best to pick an equation and variable that will be easy to deal with. This means we should try to avoid fractions if at all possible.



In this case it looks like it will be really easy to solve the first equation for y so let’s do that.





Now, substitute this into the second equation.





This is an equation in x that we can solve so let’s do that.





So, there is the x portion of the solution.



Finally, do NOT forget to go back and find the y portion of the solution. This is one of the more common mistakes students make in solving systems. To so this we can either plug the x value into one of the original equations and solve for y or we can just plug it into our substitution that we found in the first step. That will be easier so let’s do that.







So, the solution is and as we noted above.



(b) With this system we aren’t going to be able to completely avoid fractions. However, it looks like if we solve the second equation for x we can minimize them. Here is that work.





Now, substitute this into the first equation and solve the resulting equation for y.





Finally, substitute this into the original substitution to find x.

Answer 3

the graph of a lineair equation is just a line.

two lines with the same slope are either ther same line and you r system will have infinitely many solutions ( each point on the line is one )

or you will have no solutions at all since the lines have no points in common.

Answer 4

now and lower back. because of the fact the lines are linear, there can by no skill be extra suitable than one answer, despite the fact that this is available that the two lines lie in distinctive planes and could no longer intersect, and this is available that the intersection ingredient will lie exterior of the gadget barriers, and as a result no longer be interior the answer set. wherein case, there is basically no longer a answer "interior the gadget." while you're coping with basically 2 dimensions in Euclidian area, and the gadget barriers are infinite, then the respond is "constantly."

Answer 5

This is false, if two linear eqns have the same slope they are either parallel lines (no solution) or the same line (infinite solutions).

Ex:

y=3x+1
y=3x+2 >>> This is an example of a system of parallel lines

x+y=1
2x+2y=2 >>> The same line

Answer 6

No. If they have the same slope and the same y intercept then they are actually the same line and have an infinite number of solutions.

Answer 7

same slope=paralell........aka...they will never cross...aka NO SOLUTION