Question

Coretta wants to create a system of equations so that the system has only one solution. Which of these can Coretta do? Check all that apply.
Create a pair of equivalent equations.
Create a pair of lines in which one line lies directly on top of the other.
Create a pair of equations with different slopes.
Create a pair of lines that will always stay the same distance apart.
Create a pair of lines that intersect at only one point.

Answer 1

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.

Answer 2

3 and 5 are the correct choices. as long as the 2 lines have different slopes they intersect at only one point