Final answer:
The system of linear equations 3y = 4x + 1 and 8x - 2y = 10 is solved using the substitution method, yielding the solution x = 2 and y = 3.
Step-by-step explanation:
The student's question involves solving a system of linear equations using the substitution method. The given system of equations is:
To use the substitution method, first solve one of the equations for one variable in terms of the other. Let's solve the first equation for y:
y = (4x + 1) / 3
Now substitute this expression for y into the second equation:
8x - 2((4x + 1) / 3) = 10
Expand and solve this equation for x:
8x - (8x + 2) / 3 = 10
24x - 8x - 2 = 30
16x = 32
x = 2
Now that we have x, substitute it back into the first equation to find y:
y = (4(2) + 1) / 3
y = 9 / 3
y = 3
So the solution to the system of equations is x = 2, y = 3.