Question

Solve the system of equations.

6d + 3f = 12
2d = 8 ­- f

a. d= 3, f = 2
b. d = 3, f = 14
c. no solution
d. infinite solutions

Answer 1

c. No Solution.

Explanation:

6d + 3f = 12

2d = 8 ­- f

Rearranging the second equation:

2d + f = 8 Multiply this equation by 3:

6d + 3f = 24

Note that the left side of this equation = the left side of the first equation but the right sides are different. So this system does not make sense and there are No Solutions.

Answer 2

c. no solution

Explanation:

6d + 3f = 12

2d = 8 ­- f

Multiply the second equation by 3

3*2d = 3(8-f)

6d = 24-3f

Substitute into the first equation for 6d

(24-3f) +3f = 12

Combine like terms

24 =12

This is never true, so there are no solutions