Algebra Test Systems of Equations 3

Question 1

Two numbers have a sum of 20 and a difference of 6. What are the numbers?

Accepted Answer

13 and 7

Answer

x + y = 20 and x - y = 6 gives 2x = 26, so x = 13 and y = 7.

Question 2

Solve: 2x + y = 8 and x + 2y = 7

Accepted Answer

x = 3, y = 2

Answer

Substitute y = 8 - 2x into the second equation: x + 2(8 - 2x) = 7, giving x = 3 and y = 2.

Question 3

If two equations are identical, the system has:

Accepted Answer

Infinitely many solutions

Answer

Identical equations describe the same line, so every point on it is a solution.

Question 4

Solve: 5x + 2y = 20 and y = 5

Accepted Answer

x = 2

Answer

Substitute y = 5: 5x + 10 = 20, so 5x = 10 and x = 2.

Question 5

Which method is most efficient when one equation is already solved for a variable?

Accepted Answer

Substitution

Answer

Substitution is most efficient when a variable is isolated and can be plugged directly into the other equation.

Algebra Test Practice Test