Question

Solve the system of linear equations.

x+y=12
2x−2y=10
​a) (x,y)=(6,6)
b) (x,y)=(2,10)
c) (x,y)=(8,4)
d) (x,y)=(4,8)

Answer 1

The solution to the given system of linear equations is not among the options provided. By using the elimination method, it is found that (x, y) equals (8.5, 3.5), which differs from the answer choices. There may be an error in the problem or the calculation.

Step-by-step explanation:

To solve the system of linear equations given by x + y = 12 and 2x - 2y = 10, we can use the method of substitution or elimination. Let's use elimination in this case.

First, the second equation can be simplified by dividing every term by 2, leading to x - y = 5. Now we have:

• 
  
• 
  

Adding these two equations together cancels out the y variable:

2x = 17

Divide both sides by 2 to find the value of x:

x = 8.5

Now that we have x, we substitute it back into either of the original equations to find y. Let's use the first equation:

8.5 + y = 12

Subtract 8.5 from both sides:

y = 12 - 8.5

y = 3.5

Therefore, the solution is (x, y) = (8.5, 3.5), which is not listed in the options provided. It is important to note that if the answer choices are limited to integers, as in the options provided (a-d), there might have been an error in the question or calculation, and it would be advisable to recheck the problem or consult the instructor.