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
A indicates that the two lines must cross at some intersection. B tips you off to parallel lines that have the same slope and can never touch. C means that it is one and the same line.
To find the solution to this system of equations, let's simplify the equations first:
1) 6x - 4y = 20
2) 4y - 6x = -20
Notice that both equations have the same coefficients but different constants on both sides. This indicates that these equations are the same line, just rearranged.
To confirm this, let's manipulate equation 1:
1) 6x - 4y = 20
Rearranging the equation to isolate y:
6x - 20 = 4y
(6x - 20)/4 = y
3/2x - 5 = y
Now, compare it to equation 2 (4y - 6x = -20):
4y - 6x = -20
Rearranging the equation to isolate y:
4y = 6x - 20
y = (6x - 20)/4
y = 3/2x - 5
As you can see, both equations represent the same line: y = 3/2x - 5. This means that the system of equations has infinitely many solutions.
Therefore, the correct answer is C) Infinitely many solutions.