solve the following system of equations graphically on the set of axes below. \n$y = \\frac{1}{5}x - 8$\n$y…

solve the following system of equations graphically on the set of axes below. \n$y = \\frac{1}{5}x - 8$\n$y = -\\frac{4}{5}x - 3$\nplot two lines by clicking the graph. \nclick a line to delete it.

solve the following system of equations graphically on the set of axes below. \n$y = \\frac{1}{5}x - 8$\n$y = -\\frac{4}{5}x - 3$\nplot two lines by clicking the graph. \nclick a line to delete it.

Answer

Explanation:

Step1: Find intersection by solving equations

Set (\frac{1}{5}x - 8=-\frac{4}{5}x - 3). Add (\frac{4}{5}x) to both sides: (\frac{1}{5}x+\frac{4}{5}x - 8=-\frac{4}{5}x+\frac{4}{5}x - 3), which simplifies to (x - 8=- 3). Add 8 to both sides: (x - 8 + 8=-3 + 8), so (x = 5).

Step2: Substitute x into one equation

Substitute (x = 5) into (y=\frac{1}{5}x - 8): (y=\frac{1}{5}\times5 - 8=1 - 8=-7).

Answer:

The solution is ((5, -7)) (the point of intersection of the two lines). To graph:

  • For (y=\frac{1}{5}x - 8), when (x = 0), (y=-8); when (x = 5), (y=-7). Plot ((0, -8)) and ((5, -7)) and draw the line.
  • For (y=-\frac{4}{5}x - 3), when (x = 0), (y=-3); when (x = 5), (y=-7). Plot ((0, -3)) and ((5, -7)) and draw the line.