Question

Tell whether the system has one​ solution, infinitely many​ solutions, or no solution.

−x+6y=−4
4x−24y=16​

Answer 1

We can solve this system of equations using elimination method as follows:

Multiply the first equation by 4 to eliminate x:

-4x + 24y = -16

Add this equation to the second equation:

0x + 0y = 0

The resulting equation 0 = 0 is always true, regardless of the values of x and y. This means that the two original equations are equivalent and represent the same line in the coordinate plane.

Therefore, the system has infinitely many solutions, corresponding to all the points on the line represented by the equations.