Question

What is the solution to this system of equations?

x = 12 - y
2x + 3y = 29
a) x = 8, y = 4
b) x = 6, y = 6
c) x = 7, y = -5
d) x = 9, y = 3

Answer 1

Upon solving the system of equations using the substitution method, the correct solution is x = 7, y = 5. However, this solution is not among the provided options, indicating a potential error in the question or answer choices.

Step-by-step explanation:

The solution to the system of equations x = 12 - y and 2x + 3y = 29 can be found through substitution or elimination method. Let's use the substitution method:

• First, take the value of x from the first equation and substitute it into the second equation.
• So, substituting x = 12 - y into 2x + 3y = 29, we get 2(12 - y) + 3y = 29.
• Simplify this to 24 - 2y + 3y = 29, which simplifies further to y = 5.
• Now substitute y = 5 back into the first equation, x = 12 - y, which gives us x = 12 - 5, yielding x = 7.

Therefore, the solution to the system of equations is x = 7, y = 5. However, this solution is not listed among the options provided, and none of the options (a), (b), (c), or (d) are correct.