Question

Graph the solution to the following system of inequalities in the coordinate plane.

y>1/4x+6
y>2x-1

Answer 1

The solution is any point in the common part of red and blue

The two lines intersect each other at (4 , 7)

Explanation:

∵ y > 1/4 x + 6 ⇒ y = 1/4 x + 6

∵ y > 2x - 1 ⇒ y = 2x - 1

∴ 2x - 1 = 1/4 x + 6

∴ 2x - 1/4 x = 6 + 1

∴ 7/4 x = 7 ⇒ x = 7 ÷ 7/4

∴ x = 4

∴ y = 2(4) - 1 = 7

∴ The two lines intersect each other at (4 , 7)

∴ The solution is any point in the common part of red and blue