Final answer:
To solve the system of equations 8x + 5y = 24 and y = -4x by substitution, substitute y from the second equation into the first, solve for x, and then find y. The solution is x = -2 and y = 8.
Step-by-step explanation:
To solve the system of equations by substitution, follow these steps:
- Identify the simpler equation to manipulate. In this case, y = -4x is simpler.
- Substitute y from the second equation into the first one, resulting in 8x + 5(-4x) = 24.
- Simplify and solve for x: 8x - 20x = 24 leads to -12x = 24, so x = -2.
- Substitute x = -2 back into the second equation to find y: y = -4(-2), so y = 8.
- Check the solution by plugging x and y back into both original equations to verify that they hold true.
The solution to the system of equations is x = -2 and y = 8.