Question

WILL PICK BEST ANSWER IF ITS CORRECT TO ANSWER THESE FEW PROBLEMS

YOU MUST EXPLAIN WHY YOU KNOW

1)Which system of linear inequalities is represented by the graph?
(goes with pic 1)
y > 2/3x + 3 and y < -1/3x + 2
y > 2/3x + 3 and y < -1/3x + 2
y > 2/3x + 3 and y > -1/3x + 2
y > 2/3x + 3 and y >-1/3 x + 2

2)
Which system of linear inequalities is represented by the graph?
(goes with pic 2)
y > 2x – 1 and y < 2x + 2
y > 2x + 2 and y < 2x – 1
y < 2x + 2 and y > 2x – 1
y < 2x + 1 and y > 2x – 2

3)Which linear inequality is represented by the graph?
(goes with pic 3)
y > 2x + 2
y ≥ 1/2x + 1
y > 2x + 1
y ≥ 1/2x + 2

4)
What is the solution to the system of linear equations?
(goes with pic 4)
(–3, 0)
(–3, 3)
(0, 2)
(3, 1)

Answer 1

Part 1)

In this problem we have two lines

The equation of the fist line is

`y=(2)/(3)x+3`

The solution is the shaded area above the dashed line

so

the inequality is

`y>(2)/(3)x+3`

The equation of the second line is

`y=-(1)/(3)x+2`

The solution is the shaded area below the full line

so

the inequality is

`y\leq -(1)/(3)x+2`

therefore

the answer Part 1) is

`y>(2)/(3)x+3` and
`y\leq -(1)/(3)x+2`

Part 2)

In this problem we have two lines

The equation of the fist line is

`y=2x+2`

The solution is the shaded area above the full line

so

the inequality is

`y\geq 2x+2`

The equation of the second line is

`y=2x-1`

The solution is the shaded area below the full line

so

the inequality is

`y\leq 2x-1`

therefore

the answer Part 2) is

`y\geq 2x+2` and
`y\leq 2x-1`

Part 3)

In this problem we have only one line

The equation of the line is

`y=2x+1`

The solution is the shaded area above the dashed line

so

the inequality is

`y>2x+1`

therefore

the answer Part 3) is

`y>2x+1`

Part 4)

we know that

the solution of the system of linear equations is the intersection both graphs

so

see the graph

the solution point is
`(0,2)`

therefore

the answer part 4) is the option

`(0,2)`