Algebra Test Systems of Equations

Question 1

Solve: x + y = 10 and x - y = 4

Accepted Answer

x = 7, y = 3

Answer

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:

Accepted Answer

Parallel

Answer

No solution means the lines are parallel and never intersect.

Question 3

Solve by substitution: y = 2x and x + y = 9

Accepted Answer

x = 3, y = 6

Answer

Substitute y = 2x: x + 2x = 9, so x = 3 and y = 6.

Question 4

A consistent dependent system has:

Accepted Answer

Infinitely many solutions

Answer

A consistent dependent system represents the same line, giving infinitely many solutions.

Question 5

Solve: 2x + 3y = 12 and x = 3

Accepted Answer

y = 2

Answer

Substitute x = 3: 6 + 3y = 12, so 3y = 6 and y = 2.

Algebra Test Practice Test