6x + 18y = 0 4x – 12y = 20 After applying the linear combination method, Heather arrived at the equation 0 = 60. What conclusion can be drawn about the system of equations
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6x+18y=0 and 4x-12y=0 are two homogenous equations.
They can be simplified as follows.
6x+18y=0------------x+3y=0---------------eqn(1)
4x-12y=0-------------x-3y=0----------------eqn(2)
slope of x+3y=0 is (-1/3)
slope of x-3y=0 is 1/3
As the product of slopes is (-1), these two lines are perpendicular to each other.
As the lines are homogenous, (x,y)=(0,0) is a solution.
Thus the system of equations is consistent.
They can be simplified as follows.
6x+18y=0------------x+3y=0---------------eqn(1)
4x-12y=0-------------x-3y=0----------------eqn(2)
slope of x+3y=0 is (-1/3)
slope of x-3y=0 is 1/3
As the product of slopes is (-1), these two lines are perpendicular to each other.
As the lines are homogenous, (x,y)=(0,0) is a solution.
Thus the system of equations is consistent.
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