Answer:
[tex]x < \frac{20}{17}[/tex] and [tex]y \ge \frac{-5}{17}[/tex]
Step-by-step explanation:
Given
[tex]y>4 x-5\hspace{50px}y\ge\frac{3}{5} x-1[/tex]
Required
Find x and y
In the second equation. Assume that:
[tex]y = \frac{3}{5}x - 1\\[/tex]
Substitute [tex]y = \frac{3}{5}x - 1[/tex] in the first equation
[tex]y > 4x - 5[/tex]
[tex]\frac{3}{5}x - 1 > 4x - 5[/tex]
Collect like terms
[tex]\frac{3}{5}x - 4x > - 5 + 1[/tex]
[tex]\frac{3}{5}x - 4x > -4[/tex]
Multiply through by 5
[tex]3x - 20x > -20[/tex]
[tex]-17x > -20[/tex]
Solve for x
[tex]x < \frac{20}{17}[/tex]
Substitute this value of x in [tex]y \ge \frac{3}{5}x - 1[/tex]
[tex]y \ge \frac{3}{5}*\frac{20}{17} - 1[/tex]
[tex]y \ge \frac{3}{1}*\frac{4}{17} - 1[/tex]
[tex]y \ge \frac{12}{17} - 1[/tex]
[tex]y \ge \frac{12- 17}{17}[/tex]
[tex]y \ge \frac{-5}{17}[/tex]
