Answer:
option 3 and 5 are correct i.e.
3) Create a pair of equations with different slopes.
5) Create a pair of lines that intersect at only one point.
Step-by-step explanation:
Since for a system of equations to have a unique solution we must have the following properties:
1)
if we will create a pair of equivalent equations then we can't get a unique value of x and y we will get that either x is depending on y or y is depending on x i.e. we will have a variable equation.
Hence option 1) is not correct.
2)
Create a pair of lines in which one line lies directly on top of the other.
If such a case happens than also we have same equation for both the lines and like 1) we do not get a unique solution.
Hence option 2) is not correct.
3)
Create a pair of equations with different slopes.
such a case will help us to get a unique solution since we will be able to solve the system of equations by means of method of elimination.
Hence, option 3) is correct.
4)
Create a pair of lines that will always stay the same distance apart.
If such a case will happen than that means the two lines are parallel and hence the equations are equivalent.
Hence, option 4) is incorrect.
5)
Create a pair of lines that intersect at only one point.
if such a condition is true than the intersection point is the value of x and y.
hence we will get a unique value.
Hence, option 5) is true.
