Which of the following is not a possible number of solutions to a system of linear equations? A. no solution
B. 1 solution
C. 2 solutions
D. infinitely-many solutions

A system of linear equations cannot have 2 solutions.

Step-by-step explanation:

If we were to be given a system of linear equations, we could graph them to see if they had intersection points or not.

Let's look at three circumstances.

System One - No Solution

We can solve this system by multiply the second equation by 2.

Now, our system becomes:

Now, we can add our equations together.

We get a false statement. When you get a false statement with systems, this means that there is no solution for the equations.

System Two - One Solution

We are given two systems that can be solved by elimination.

Our new system is:

Now, we can add the equations together.

Now, we substitute this value of y into either equation and solve for x.

Therefore, there is one solution at (1, -2).

System Three - Infinitely-Many Solutions

This system of equations needs simplified first before any action can be taken. We need to place the second equation in slope-intercept form.

Now, our system becomes:

We can already see that there is no way to add or subtract without getting 0 = 0. Therefore, for any value of y or x, this system of equations has a solution. This means that the solution has infinitely-many solutions.

Because there is a way to have no solution, 1 solution, and infinitely-many solutions, it has become apparent that there is no way for a linear system of equations to have 2 solutions.

A quadratic system of equations could have 2 solutions. However, because we are dealing with linear equations, we cannot have 2 solutions.

by definition, an arc subtended by a central angle of some given measure has the same measure. so .

yes because they have the same amount of green and blur marbles.

step-by-step explanation: