Question

Drag each tile to the correct box. Arrange the systems of equations that have a single solution in increasing order of the x-values in their solutions.

A. 2x + y = 10; x − 3y = -2
B. x + 2y = 5; 2x + y = 4
C. x + 3y = 5; 6x − y = 11
D. 2x + y = 10; -6x − 3y = -2

Answer 1

Solving each system of equations individually, we find that the x-values for their single solutions are 2 for Systems A, B, and C, and 4 for System D. The systems can be arranged in increasing order of their x-values, which is A, B, C, and then D.

Step-by-step explanation:

The student is asked to arrange systems of equations that have a single solution based on the x-values in their solutions. To do this, we can solve each system individually and find the value of x for each one.

1. For System A (2x + y = 10; x − 3y = -2), we can solve by substitution or elimination. Solving these equations, we find that the solution is x = 2, y = 6.
2. For System B (x + 2y = 5; 2x + y = 4), using similar methods, the solution is x = 2, y = 1.5.
3. For System C (x + 3y = 5; 6x − y = 11), solving yields x = 2, y = 1.
4. For System D (2x + y = 10; -6x − 3y = -2), we find the solution to be x = 4, y = 2.

Now, we can arrange these systems in increasing order of the x-values of their solutions, which are all x = 2 except for System D which has x = 4. Therefore, the order is A, B, C (all have x = 2 and thus are equivalent in terms of x), followed by D, which has the largest x-value.