Question

Solve the following system of equations by substitution. *
8x + 5y = 24
y = -4x

Answer 1

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:

1. Identify the simpler equation to manipulate. In this case, y = -4x is simpler.
2. Substitute y from the second equation into the first one, resulting in 8x + 5(-4x) = 24.
3. Simplify and solve for x: 8x - 20x = 24 leads to -12x = 24, so x = -2.
4. Substitute x = -2 back into the second equation to find y: y = -4(-2), so y = 8.
5. 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.