10
QuizMultiple Choice

Solving Systems of Linear Equations: Linear Combinations — Quiz

Question 10 • Algebra I

The system of equations shown is solved using the linear combination method 6 x minus 5 y is equal to negative 8 which is same as 6 x minus 5 y is equal to negative 8 which is same as 6 x minus 5 y is equal to negative 8; negative 24 x plus 20 y is equal to 32 which is same as 1 fourth times negative 24 x plus 20 y is equal to 32 which is same as negative 6 x plus 5 y is equal to 8; 6 x minus 5 y is equal to negative 8 is added to 6 x plus 5 y is equal to 8 which results 0 is equal to 0 What does 0 is equal to 0 mean regarding the solution to the system?

Answer
A
There are infinitely many solutions to the system because the equations represent the same line.
B
There are infinitely many solutions to the system because the equations represent parallel lines.
C
There are no solutions to the system because the equations represent the same line.
D
There are no solutions to the system because the equations represent parallel lines.

Explanation

Multiplying the second equation, −24x + 20y = 32, by 1/4 gives −6x + 5y = 8. This is the first equation, 6x − 5y = −8, multiplied by −1, so both equations describe the same line. The result 0 = 0 is a true statement and means the equations do not determine a single point; there are infinitely many solutions on that line.

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