3
QuizMultiple Choice

Solving Systems of Linear Equations: Linear Combinations — Quiz

Question 3 • Algebra I

Which statement is true about the equations negative 3 x plus 4 y is equal to 12 and 1 fourth x minus 1 third y is equal to 1 ?

Answer
A
The system of the equations has exactly one solution at negative 4 comma 3 .
B
The system of the equations has an infinite number of solutions represented by either equation.
C
The system of the equations has exactly one solution at negative 8 comma 3 .
D
The system of the equations has no solution; the two lines are parallel.

Explanation

Multiply the second equation by 12 to clear its fractions: 3x − 4y = 12. Multiplying the first equation by −1 gives 3x − 4y = −12. The equations have the same left-hand side but different constants, so they represent distinct parallel lines and have no solution. The true statement is that the system has no solution because the lines are parallel.

AI-written and checked against the verified answer.

Previous
Next