The treatment of a certain viral disease requires a combination dose of drugs D1 and D2. Each unit of D1 contains 1 milligram of factor X and 2 milligrams of factor Y, and each unit of D2 contains 2 milligrams of factor X and 3 milligrams of factor Y. If the most effective treatment requires 13 milligrams of factor X and 22 milligrams of factor Y, how many units of D1 and D2 should be administered to the patient.

I know that I have to form at least two equations from this problem because I have to use the substitution or elimination method to solve this problem. I know that the answers are: D1=5 and D2=4 but I don't know what equations to form and what to substitute or eliminate

Let G be the number of "Units" of D1 and H be the number of un its of D2.

The equations you have to satisfy are:
G + 2H = 13(the amount of drug X needed)
2G + 3H = 22 (the amount of drug Y needed).
2G + 4H = 26
H = 4
G = 13 - 8 = 5

To solve this problem, let's represent the number of units of D1 administered as "x" and the number of units of D2 administered as "y."

From the problem statement, we know that each unit of D1 contains 1 milligram of factor X and 2 milligrams of factor Y, and each unit of D2 contains 2 milligrams of factor X and 3 milligrams of factor Y.

Equation 1: To find the total amount of factor X administered, we multiply the number of units of D1 (x) by the amount of factor X in D1 (1 milligram) and multiply the number of units of D2 (y) by the amount of factor X in D2 (2 milligrams). This gives us the equation: 1x + 2y = 13 (since the total amount of factor X required is 13 milligrams).

Equation 2: To find the total amount of factor Y administered, we multiply the number of units of D1 (x) by the amount of factor Y in D1 (2 milligrams) and multiply the number of units of D2 (y) by the amount of factor Y in D2 (3 milligrams). This gives us the equation: 2x + 3y = 22 (since the total amount of factor Y required is 22 milligrams).

Now we have a system of linear equations:
1x + 2y = 13
2x + 3y = 22

To solve this system of equations, you can use the substitution or elimination method. Let's use the substitution method.

Solve Equation 1 for x:
x = 13 - 2y

Substitute this expression for x in Equation 2:
2(13 - 2y) + 3y = 22

Simplify and solve for y:
26 - 4y + 3y = 22
-y = -4
y = 4

Substitute that value back into Equation 1 to solve for x:
x = 13 - 2(4)
x = 13 - 8
x = 5

Therefore, the solution is x = 5 (units of D1) and y = 4 (units of D2).