Question

Solve the systems of equations and inequalities :

x - y = -9
3x + 4y = 8

a) x = -5, y = -14
b) x = -9, y = 0
c) x = 5, y = -14
d) x = 9, y = 0

Answer 1

Upon solving the system of equations, we find the answers to be x = -4 and y = 5, which does not match any of the provided answer choices, suggesting a potential error in calculation or the provided options.

Step-by-step explanation:

First, we need to solve the system of linear equations given by:

• x - y = -9
• 3x + 4y = 8

We can use substitution or elimination. Let's use substitution here.

1. Solve the first equation for x: x = y - 9.
2. Substitute x into the second equation: 3(y - 9) + 4y = 8.
3. Combine like terms: 3y - 27 + 4y = 8.
4. Add 27 to both sides: 3y + 4y = 35.
5. Combine like terms: 7y = 35.
6. Divide both sides by 7: y = 5.
7. Substitute y back into x = y - 9 to find x: x = 5 - 9.
8. Therefore, x = -4.

However, none of the answer choices match our solution of x = -4 and y = 5. Therefore, there might have been an error in the calculation or in the answer choices provided.