Question

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

-X-5y = -6
y = 6x-5
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
• A. The system has a single solution. The solution set is O. (Type an ordered pair.)
B. There are infinitely many solutions and the equations are dependent. The solution set is {(x,y)} (Type an ordered pair.)
C. The system is inconsistent. The solution set is the empty set

Answer 1

The (single) solution is (1, 1).

Explanation:

The second equation tells us that y = 6x-5. Substitute this 6x - 5 into the first equation, as follows: -x - 5(6x - 5) = -6

Then -x - 30x + 25 = -6. Combining like terms, we get -31x = -31, so that x = 1. Subbing this result into the second equation, we find y: y = 6(1) - 5 = 1. The solution is (1, 1).