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.

A. Create a pair of equivalent equations.
B. Create a pair of lines in which one line lies directly on top of the other.
C. Create a pair of equations with different slopes.
D. Create a pair of lines that will always stay the same distance apart.
E. Create a pair of lines that intersect at only one point.

Answer 1

C and E

Explanation:

I took the test.

Answer 2

C. Create a pair of equations with different slopes. ( Holds only if the equations are linear, otherwise they can have more than one solution)

E. Create a pair of lines that intersect at only one point.

Explanation:

Intersection points of two lines are the solutions for the equation, because intersection points satisfy both equations.

Also assuming the equations are linear, creating a pair of equations with different slopes has one solution as the example below:

assume line1 is ax+b and line2 is cx+d

then ax+b=cx+d has a solution at x=(d-b)/(a-c) given that a≠c