Question

Which point would be a solution to the system of linear inequalities shown below? y>4 x-5\hspace{50px}y\ge\frac{3}{5} x-1 y>4x−5y≥ 5 3 ​ x−1

Answer 1

Answer:

$x < \frac{20}{17}$ and $y \ge \frac{-5}{17}$

Step-by-step explanation:

Given

$y>4 x-5\hspace{50px}y\ge\frac{3}{5} x-1$

Required

Find x and y

In the second equation. Assume that:

$y = \frac{3}{5}x - 1$

Substitute $y = \frac{3}{5}x - 1$ in the first equation

$y > 4x - 5$

$\frac{3}{5}x - 1 > 4x - 5$

Collect like terms

$\frac{3}{5}x - 4x > - 5 + 1$

$\frac{3}{5}x - 4x > -4$

Multiply through by 5

$3x - 20x > -20$

$-17x > -20$

Solve for x

$x < \frac{20}{17}$

Substitute this value of x in $y \ge \frac{3}{5}x - 1$

$y \ge \frac{3}{5}*\frac{20}{17} - 1$

$y \ge \frac{3}{1}*\frac{4}{17} - 1$

$y \ge \frac{12}{17} - 1$

$y \ge \frac{12- 17}{17}$

$y \ge \frac{-5}{17}$