Question

Percy said that any real number for k would cause the system of equations to have no solution. Explain the error in Percy’s statement.
6x + 4y = 14,

3x + 2y = k

Answer 1

Answer:

Except k=7, any real number for k would cause the system of equations to have no solution.

Step-by-step explanation:

In general a system of equations can be represented as ax+by=c and dx+ey=f. In order this system of equations to have NO SOLUTIONS a/d=b/a≠c/f. In our example a=6, b=4, c=14, d=3, e=2 and f=k. To apply the formula above, 6/3=4/2≠14/k. Hence k≠7. It can be concluded that except k=7, any real number for k would cause the system of equations to have no solutions.

Just for information, if k=7 the system will have infinitely many solutions.

Answer 2

Sample Response: k = 7 proves the equations are equivalent and, therefore, have infinitely many solutions. That is illustrated by the fact that multiplying 2 by 3x +2y = 7 will create the equivalent of 6x + 4y =14.