Math Homework Help

Question

Two system of equations are given. For each system choose if it's infinite solutions,no solution,or one solution. If it's one solution provide the answer.

x+4y=5

-x+4y=3

Answer 1

Only ONE system is given in this problem. Evaluate the principal determinant and make sure it is not zero.

D = (1)(4) - (-1)(4) ≠ 0 ⇒ one solution

Add the 2 equations and get

8y = 8

y = 1

Plug this value of y into either equation and get

x = 1

Test the solution.

Answer 2

Only ONE system is given in this problem. Evaluate the principal determinant and make sure it is not zero.

D = (1)(4) - (-1)(4) ≠ 0 ⇒ one solution

Add the 2 equations and get

8y = 8

y = 1

Plug this value of y into either equation and get

x = 1

Test the solution.