Vineet solved a system of equations by substitution. In his work, he substituted an expression for one of the variables and solved for the value of the other. this resulted in the equation 7=9. what can vineet conclude? -a. the solution to the system is (7,9)
-b. the system of linear equations does not have a solution
-c. the work must be incorrect because it is not possible to get this equation
-d. the system of equations has infinitely many solutions

The correct option is (b) The system of equations does not have a solution.

Step-by-step explanation:

Let us understand this with the help of an example:

Consider the equations:

......(1)

and

......(2)

Now, solve this with the help of substitution method as shown:

The equation (1) can be written as:

x = 1 - y

Substitute x = 1 - y in equation (2).

9(1 - y)+ 9y = 7

9 - 9y + 9y = 7

9 = 7

Which is not true.

There is no mistake in calculation. The both equation are parallel to each other that is why there is no solution for the equation.

Hence, the correct option is (b) The system of equations does not have a solution.

The graph of these two lines is shown as in figure 1.