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QuizMultiple Select

Using Graphs to Determine the Number of Solutions

Question 1 • (AG Q4) Keystone Algebra 1 Block: 25-26 (DDiamond)

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.

Answer
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.

Explanation

A system of two linear equations has exactly one solution when the two lines intersect at one point. Different slopes guarantee that the lines cross once, so choices C and E describe systems with one solution. Equivalent equations and lines lying on top of each other represent the same line and have infinitely many solutions; lines that stay the same distance apart are parallel and have no solution.

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