Final answer:
To solve the system of equations 3-2x+8y=20 and y=2 using the substitution method, replace y with 2 in the first equation and then solve for x, which results in x=-1/2.
Step-by-step explanation:
The student's question involves solving a system of equations using the substitution method. Specifically, the student has the equations 3-2x+8y=20 and y=2. To use the substitution method, we can replace y in the first equation with the value 2 because the second equation indicates that y is equal to 2. The first equation will then become 3-2x+8(2) = 20.
After this substitution, simplifying the equation gives us 3-2x+16 = 20. Combining like terms results in -2x+19 = 20. When we solve for x, we get x = -1/2. It's important to ensure that the steps involved in using the substitution method are explained in a way that fosters understanding of this algebraic technique.
Substituting y = 2 into the first equation:
3 - 2x + 8(2) = 20
3 - 2x + 16 = 20
19 - 2x = 20
-2x = 1
x = -1/2
Therefore, the solution to the system of equations is x = -1/2 and y = 2.