Question

Match each system of linear equations with the correct number of solutions. One solution- no solution- infinitely- many solutions − 3 ⁢ x y = 7 2 ⁢ x − 4 ⁢ y = − 8 3 ⁢ x − y = 4 6 ⁢ x − 2 ⁢ y = 8 .

Answer 1

The first system has one solution, and the second system has infinitely many solutions.

Step-by-step explanation:

To determine the number of solutions for each system of linear equations, we can use the concept of slopes. If the slopes of the two lines are equal and the y-intercepts are different, the system has no solution. If the slopes and y-intercepts are equal, the system has infinitely many solutions. If the slopes are different, the system has one solution.

For the given systems of equations:

-3x + y = 7
2x - 4y = -8

The slopes of the two lines are -3 and 1/2, which are different. Therefore, the system has one solution.

3x - y = 4
6x - 2y = 8

The slopes of the two lines are both equal to 3/1 (or 3). Additionally, the y-intercepts are equal. Therefore, the system has infinitely many solutions.