Question

1.Graph the system of inequalities. Then use your graph to identify the point that represents a solution to the system. x > 3 and y ≤ 2x – 5 . A. (5, 6) B. (4, –1) C. (–3, –1) D. (1, 11) 2.Graph the system of inequalities. Then use your graph to identify the point that represents a solution to the system. x – y ≥ 7 and x + 2y < 5 A. (6,1) B. (8,-1) C. (6,2) D.(6,-2) 3.Graph the system of inequalities. Then use your graph to identify the point that represents a solution to the system. 3x – 4y > 0 and x – 5y > 0. A. (-4,-2) B. (6,0) C.(0,0) D. (6,2)

Answer 1

Part 1) we have

`x > 3`

`y \leq 2x- 5`

Step
`1`

Graph the system

using a graph tool

The solution of the system of inequalities is the shaded area

see the attached figure N
`1`

we know that the point that represents a solution to the system are inside the shaded area

Step
`2`

Graph the points

we have

`A. (5, 6) \ B. (4, -1)\ C. (-3, -1)\ D. (1, 11)`

the point that represents a solution to the system are

the solution is the point B------> see the attached figure N
`1`

Part 2) we have

`x-y \geq 7`

`x + 2y < 5`

Step
`1`

Graph the system

using a graph tool

The solution of the system of inequalities is the shaded area

see the attached figure N
`2`

we know that the point that represents a solution to the system are inside the shaded area

Step
`2`

Graph the points

we have

`A. (6,1) \ B. (8,-1)\ C. (6,2)\ D.(6,-2)`

the point that represents a solution to the system are

the solution is the point D------> see the attached figure N
`2`

Part 3) we have

`3x - 4y > 0`

`x - 5y > 0`

Step
`1`

Graph the system

using a graph tool

The solution of the system of inequalities is the shaded area

see the attached figure N
`3`

we know that the point that represents a solution to the system are inside the shaded area

Step
`2`

Graph the points

we have

`A. (-4,-2) \ B. (6,0)\ C.(0,0)\ D. (6,2)`

the point that represents a solution to the system are

the solution is the point B------> see the attached figure N
`3`