Question

2.

Identify the error that was made in the following problem when applying the linear combination method. Then correctly
solve the problem using linear combination.
Incorrect solution:
(2x + 3y - 24
2x-y-8
(2x+3y)-(2x-y)-(24-8)
2y = 16
y=8
2x + 3(8)=24
x=0
Solution: (0,8)
Description of error:
Corrected solution:
2x+3y-24
2x-y-8

Answer 1

the solution is (24,40)

Explanation:

The error in this problem is that the incorrect solution is attempting to solve for y first, by setting 2y = 16 and then solving for y as 8. However, this step is not valid when using the linear combination method to solve a system of equations.

To correctly solve the problem using linear combination, the first step would be to add the two equations together:

(2x+3y-24) + (2x-y-8) = 3x+2y-32

then solving for x:

x = (32 - 2y) / 3

Substituting x back into the first equation:

2x + 3y - 24 = 0

2((32 - 2y) / 3) + 3y - 24 = 0

64 - 4y + 3y - 24 = 0

-y = -40

y = 40

then substitute y back into the second equation:

2x - 40 - 8 = 0

2x = 48

x = 24

So the solution is (24,40)