Algebra Test Systems of Equations 2

Question 1

Solve by elimination: 3x + 2y = 16 and x - 2y = 0

Accepted Answer

x = 4, y = 2

Answer

Adding the equations gives 4x = 16, so x = 4; substituting gives y = 2.

Question 2

Two linear equations with the same slope but different y-intercepts have:

Accepted Answer

No solution

Answer

Equal slopes with different y-intercepts mean the lines are parallel with no intersection.

Question 3

Solve: y = 3x - 1 and y = x + 5

Accepted Answer

x = 3, y = 8

Answer

Set 3x - 1 = x + 5, so 2x = 6 and x = 3; then y = 8.

Question 4

What is the solution to: x + y = 7 and 2x - y = 2?

Accepted Answer

x = 3, y = 4

Answer

Adding gives 3x = 9, so x = 3; substituting gives y = 4.

Question 5

A system with exactly one solution is called:

Accepted Answer

Consistent and independent

Answer

A system with exactly one solution is consistent (a solution exists) and independent (distinct lines).

Algebra Test Practice Test