Answer:
The given equations are:
1. -6x + 18y = 0
2. 4x - 12y = -20
To apply the linear combination method, we need to eliminate one variable by multiplying each equation by a suitable constant. In this case, if we multiply the first equation by 2 and the second equation by 3, the coefficients of 'y' in both equations will become -36y, allowing us to eliminate 'y'.
After performing the multiplication, we have:
3. -12x + 36y = 0
4. 12x - 36y = -60
Now, when we add equations 3 and 4 together, we get:
-12x + 36y + 12x - 36y = 0 - 60
0 = -60
This resulting equation is 0 = -60, which is not possible. It implies that 0 is not equal to -60, leading us to conclude that the system of equations has no solution.
Therefore, the correct answer is:
The equation has no solution; therefore, the system of equations has no solution.
Step-by-step explanation:
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