Question

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 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.

Answer 1

Answer b: the system of equations does not have a solution

Suppose the systems consits of two first grade equations with two varaibles. If the two equations are parallel you would obtaing a result like Vinnet.

This is an example:

x = y + 1

7x = 7y +  9

substitue to get:

7(y+1) = 7y +9
7y + 7 = 7y + 9
7=9

There is not mistake, the system has no solutions, because the two equations represent parallel lines, which do no intercept one to each other.

Answer 2

Answer:

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:

$x+y=1$ ......(1)

and

$9x+9y=7$......(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.