6x-4y=20 and 4y-6x=-20 What is the solution of the system of equations for this problem?
A)A point
B)No solution
C)Infinitely many solutions
These points would have C correct?
Yes,
since you are in effect only given one equation.
Notice that by multiplying the second by -1 simply gives you the first equation, so the two equations are the same
Thanks Reiny
To solve the given system of equations, we can observe that both equations are essentially the same, just rearranged. This implies that they represent the same line in the coordinate plane.
If we simplify the equations, we get:
6x - 4y = 20 ----> (1)
4y - 6x = -20 ----> (2)
Rearranging equation (2), we get:
-6x + 4y = -20
If we compare this equation (3) with equation (1), we notice that equation (3) is just equation (1) multiplied by -1. This means that the two equations represent the same line, and hence they are consistent.
Since both equations represent the same line, they intersect at infinitely many points. Therefore, the solution of this system of equations is option C) Infinitely many solutions.