Answer:
Equation (c) 9x - 12y = 24 would cause a consistent-dependent system
Step-by-step explanation:
Given equation 3x − 4y = 8
We have to find the equation from the given option that would cause a consistent-dependent system.
A given system of linear equation \(a_1x+b_1y+c=0 \ and\ a_2x+b_2y+c_2=0\)
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line that is slope of both the equation will be same.
that is possible when \(a_2\) is multiple of \(a_1\) and \(b_2\) is multiple of \(b_1\) and this multiplication factor is same for both.
Thus, for the given equation 3x − 4y = 8
Only equation (c) 9x - 12y = 24 is a multiple of equation 3x − 4y = 8 with same factor of multiplication 3
Also, the slope of two equation is same \(\frac{3}{4}\)
Thus, equation (c) 9x - 12y = 24 would cause a consistent-dependent system
