Question

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how many solutions does the system of equations below have? 4x - 3y = -4 8x - 6y = -8 no solution one solution infinitely many solutions

Explanation:

Step1: Check the ratio of coefficients

For the system of linear - equations \(a_1x + b_1y=c_1\) and \(a_2x + b_2y = c_2\), here \(a_1 = 4\), \(b_1=-3\), \(c_1=-4\), \(a_2 = 8\), \(b_2=-6\), \(c_2=-8\). Calculate \(\frac{a_1}{a_2}=\frac{4}{8}=\frac{1}{2}\), \(\frac{b_1}{b_2}=\frac{-3}{-6}=\frac{1}{2}\), \(\frac{c_1}{c_2}=\frac{-4}{-8}=\frac{1}{2}\).

Step2: Determine the number of solutions

Since \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\), the two equations represent the same line. So the system has infinitely many solutions.

Answer:

infinitely many solutions