Question

Which graph shows the solution to the system of linear inequalities y>1/3x+1, y>2x-3

Answer 1

For this case we have the following system:

`y> \frac {1} {3} x + 1\\y> 2x-3`

To solve, we first change the inequality for an equality:

`y = \frac {1} {3} x + 1\\y = 2x-3`

Matching we have:

`\frac {1} {3} x + 1 = 2x-3\\\frac {1} {3} x-2x = -3-1\\- \frac {5} {3} x = -4\\\frac {5} {3} x = 4\\5x = 12\\x = \frac {12} {5}`

So:

`y = 2x-3\\y = 2 (\frac {12} {5}) - 3\\y = \frac {24} {5} -3\\y = \frac {9} {5}`

Thus,
`(\frac {12} {5}, \frac {9} {5})`is the point of intersection of the lines.

Answer:

The graphic is attached