Systems of Equations Flashcards
6 cards from real Algebra Test practice questions. Tap to flip, then mark Knew It or Still Learning โ missed cards come back until you master them.
Read the first 6 Systems of Equations flashcards as text
Solve by elimination: 3x + 2y = 16 and x - 2y = 0
Answer: x = 4, y = 2
Adding the equations gives 4x = 16, so x = 4; substituting gives y = 2.
Two linear equations with the same slope but different y-intercepts have:
Answer: No solution
Equal slopes with different y-intercepts mean the lines are parallel with no intersection.
Solve: y = 3x - 1 and y = x + 5
Answer: x = 3, y = 8
Set 3x - 1 = x + 5, so 2x = 6 and x = 3; then y = 8.
What is the solution to: x + y = 7 and 2x - y = 2?
Answer: x = 3, y = 4
Adding gives 3x = 9, so x = 3; substituting gives y = 4.
A system with exactly one solution is called:
Answer: Consistent and independent
A system with exactly one solution is consistent (a solution exists) and independent (distinct lines).
In the system y = 4x - 3 and y = 4x + 1, how many solutions exist?
Answer: None
Both lines have slope 4 but different intercepts, making them parallel with no intersection.