let

x = ounces of the 25% saline solution

y = ounces of the 30% saline solution

She needs a total of 6 ounces in the mix:

x + y = 6

Elizabeth wants to mix a 25% saline solution with a 40% saline solution to make a 30% saline solution:

0.25x + 0.40y = 0.30*6

by solving the system of equations:

x + y = 6

0.25x + 0.40y = 0.30*6

........

click here to see all the system of equations solution steps

........

x = 4 oz

y = 2 oz

Elizabeth should use 4 ounces of the 25% saline solution and 2 ounces of the 40% saline solution.