Question

Which graph shows the solution to the system of linear inequalities?

y< 2x-5
y>-3x + 1

Answer 1

See explanation

Explanation:

Plot the solution sets to both inequalities.

1. For the inequality
`y<2x+5.` First, plot the dotted line
`y=2x+5` (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.

`2\cdot 0-5=-5<0`

so the origin does not belong to the needed part. Shade the part, which does not include origin.

2. For the inequality
`y>-3x+1.` First, plot the dotted line
`y=-3x+1` (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.

`-3\cdot 0+1=1>0`

so the origin does not belong to the needed part. Shade the part, which does not include origin.

3. Find the common region of these two shaded parts - this is the solution to the system of two inequalities.