solve the following system of equations graphically on the set of axes below.\n$y = \\frac{5}{4}x - 6$\n$y =…

solve the following system of equations graphically on the set of axes below.\n$y = \\frac{5}{4}x - 6$\n$y = -\\frac{1}{2}x + 8$\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$y = \\frac{5}{4}x - 6$\n$y = -\\frac{1}{2}x + 8$\nplot two lines by clicking the graph.\nclick a line to delete it.

Answer

Explanation:

Step1: Set the equations equal

Since (y = \frac{5}{4}x - 6) and (y=-\frac{1}{2}x + 8), we set (\frac{5}{4}x-6=-\frac{1}{2}x + 8).

Step2: Solve for (x)

Multiply through by (4) to clear the fractions: (5x-24=-2x + 32). Add (2x) to both sides: (5x + 2x-24=-2x+2x + 32), so (7x-24 = 32). Add (24) to both sides: (7x-24 + 24=32 + 24), then (7x=56). Divide by (7): (x=\frac{56}{7}=8).

Step3: Solve for (y)

Substitute (x = 8) into (y=-\frac{1}{2}x + 8). (y=-\frac{1}{2}(8)+8=-4 + 8=4).

Answer:

The solution of the system is ((8,4))