Question

Which graph shows the solution to the system of inequalities below? x+y<3 -5x+2y<10

Answer 1

D) The last graph

Explanation:

Answer 2

The common shaded region in the graph, represents the solution to the system of inequalities.

Explanation:

The given inequalities are

`x+y<3` .... (1)

`-5x+2y<10` ..... (2)

The related lines of given inequalities are dotted lines, because the sing of inequalities are <.

The related equations of given inequalities are

`x+y=3` .... (3)

`-5x+2y=10` .... (4)

Find x-intercepts and y-intercepts of related equations.

Put x=0 in equations (3).

`0+y=3`

Put y=0 in equations (3).

`x+0=3`

Therefore the intercepts of equation (3) are (0,3) and (3,0).

Put x=0 in equations (4).

`-5(0)+2y=10`

`y=5`

Put y=0 in equations (4).

`-5x+2(0)=10`

`x=-2`

Therefore the intercepts of equation (3) are (0,5) and (-2,0).

Check the given inequalities by origin.

Put (0,0) in inequality (1),

`0+0<3`

`0<3`

Therefore, (0,0) lies in the shaded region of inequality (1).

Put (0,0) in inequality (2),

`-5(0)+2(0)<10`

`0<10`

Therefore, (0,0) lies in the shaded region of inequality (2).

The common shaded region in the graph, represents the solution to the system of inequalities.