Algebra Test Systems of Equations 1 — Questions and Answers
Question 1: Solve: x + y = 10 and x - y = 4
- x = 6, y = 4
- x = 7, y = 3 (Correct answer)
- x = 8, y = 2
- x = 5, y = 5
Correct answer: x = 7, y = 3
Adding the equations gives 2x = 14, so x = 7; substituting gives y = 3.
Question 2: When a system of two linear equations has no solution, geometrically the lines are:
- The same line
- Intersecting at one point
- Parallel (Correct answer)
- Perpendicular
Correct answer: Parallel
No solution means the lines are parallel and never intersect.
Question 3: Solve by substitution: y = 2x and x + y = 9
- x = 2, y = 7
- x = 3, y = 6 (Correct answer)
- x = 4, y = 5
- x = 1, y = 8
Correct answer: x = 3, y = 6
Substitute y = 2x: x + 2x = 9, so x = 3 and y = 6.
Question 4: A consistent dependent system has:
- No solution
- Exactly one solution
- Exactly two solutions
- Infinitely many solutions (Correct answer)
Correct answer: Infinitely many solutions
A consistent dependent system represents the same line, giving infinitely many solutions.
Question 5: Solve: 2x + 3y = 12 and x = 3
- y = 1
- y = 2 (Correct answer)
- y = 3
- y = 4
Correct answer: y = 2
Substitute x = 3: 6 + 3y = 12, so 3y = 6 and y = 2.
Question 6: Which method eliminates a variable by adding or subtracting equations?
- Graphing
- Substitution
- Elimination (Correct answer)
- Factoring
Correct answer: Elimination
The elimination method adds or subtracts equations to cancel one variable.
Algebra Test Systems of Equations 1
Solve: x + y = 10 and x - y = 4