X - 4y = -1
3x + 5y = 31

9514 1404 393

  (x, y) = (7, 2)

Step-by-step explanation:

We assume you want the solution to this system of equations.

Since you're seeking help from "technology", it is appropriate to use the technology of a graphing calculator to find the solution. The attachment shows it to be (x, y) = (7, 2).

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The coefficient of x in the first equation is 1, so it is convenient to use that equation to write an expression for x:

  x = 4y -1 . . . . . add 4y to the equation

  3(4y -1) +5y = 31 . . . . substitute for x in the second equation.

  17y = 34 . . . . . . . . . . . simplify, add 3

  y = 2 . . . . . . . . divide by 17

  x = 4(2) -1 = 7 . . . . use the equation above to find x

The solution is (x, y) = (7, 2).

a. she will receive a refund of $278.

step-by-step explanation: