which value, when placed in the box, would result in a system of equations with infinitely many…

which value, when placed in the box, would result in a system of equations with infinitely many solutions?\n$y = 2x - 5$\n$2y - 4x = square$\n-10\n-5\n5\n10

which value, when placed in the box, would result in a system of equations with infinitely many solutions?\n$y = 2x - 5$\n$2y - 4x = square$\n-10\n-5\n5\n10

Answer

Explanation:

Step1: Rearrange the first equation

Given (y = 2x-5), multiply both sides by (2) to get (2y=4x - 10). Then, rearrange it to the form (2y-4x=- 10).

Step2: Analyze the system of equations

For a system of linear equations (a_1x + b_1y=c_1) and (a_2x + b_2y=c_2) (here (a_1=-4), (b_1 = 2), (c_1=\square), (a_2=-4), (b_2 = 2), (c_2=-10) after rearrangement of the first equation), if (\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}) (in non - zero denominators case, here (a_2=-4\neq0), (b_2 = 2\neq0)), the system has infinitely many solutions.

Answer:

A. (-10)