Use elimination to solve the system of equations, if possible. Identify the syst

Question

Use elimination to solve the system of equations, if possible. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. x + 4y = 19 x - 2y = -5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The solution is There is a unique solution so the system is consistent and the equations are independent. (Simplify your answer. Type an ordered pair.) The system has infinitely many solutions of the form {(x, y)}and is consistent. The equations are dependent. (Type an equation.) There are no solutions. The system is inconsistent.

Explanation / Answer

x+4y = 19 ----------------- equation 1

x - 2y = -5 ------------------- equation 2

multiplyinh equation 2 by -1 and adding eqiation 1 to it

x + 4y = 19

-x + 2y = 5

------------------------

0 + 6y = 24

dividing both sides by 6

y = 4

plugging y = 4 in equation 1

x + 4(4) = 19

x = 19-16

x = 3

solution is

x = 3

y = 4

( option a is correct )

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