Final answer:
To solve the system using the substitution method, solve for one variable and substitute it into the other equation. The solution is x ≈ 273.35 and y ≈ 816.59.
Step-by-step explanation:
To solve the system of linear equations using the substitution method, we need to solve for one variable and substitute it into the other equation. Let's solve for y in the first equation.
y + 0.415x = 930
y = 930 - 0.415x
Now we can substitute y into the second equation:
y = 3x - 5
Substituting (930 - 0.415x) into the second equation:
(930 - 0.415x) = 3x - 5
Now we can solve for x:
930 - 0.415x = 3x - 5
Combine like terms:
930 + 5 = 3x + 0.415x
935 = 3.415x
Divide both sides by 3.415:
x = 935 / 3.415
Simplify:
x ≈ 273.35
Now we can substitute x back into the first equation to find y:
y + 0.415(273.35) = 930
Combine like terms:
y + 113.41 = 930
Subtract 113.41 from both sides:
y = 930 - 113.41
Simplify:
y ≈ 816.59
Therefore, the solution to the system of linear equations is x ≈ 273.35 and y ≈ 816.59.