Question

Please help! i dont understand

Answer 1

QUESTION 1

The given inequality is

`y\leq x-3` and
`y\geq -x-2`.

If (3,-2) is a solution; then it must satisfy both inequalities.

We put x=3 and y=-2 in to both inequalities.

`-2\leq 3-3` and
`-2\geq -3-2`.

`-2\leq 0`:True and
`-2\geq -5`:True

Both inequalities are satisfied, hence (3,-2) is a solution to the given system of inequality.

QUESTION 2

The given inequality is

`y\:>\:-3x+3` and
`y\:>\: x+2`.

If (1,4) is a solution; then it must satisfy both inequalities.

We put x=1 and y=4 in to both inequalities.

`4\:>\:-3(1)+3` and
`4\:>\: 1+2`.

`4\:>\:0`:True and
`4\:>\: 3`:True

Both inequalities are satisfied, hence (1,4) is a solution to the given system of inequality.

Ans: True

QUESTION 3

The given inequality is

`y\leq 3x-6` and
`y\:>\: -4x+2`.

If (0,-2) is a solution; then it must satisfy both inequalities.

We put x=0 and y=-2 in to both inequalities.

`-2\leq 3(0)-6` and
`-2\:>\: -4(0)+2`.

`-2\leq -6`:False and
`-2\:>\:2`:False

Both inequalities are not satisfied, hence (0,-2) is a solution to the given system of inequality.

Ans:False

QUESTION 4

The given inequality is

`2x-y\:<\: 4` and
`x+y\:>\:-1`.

If (0,3) is a solution; then it must satisfy both inequalities.

We put x=0 and y=3 in to both inequalities.

`2(0)-3\:<\: 4` and
`0+3\:>\:-1`.

`-3\:<\: 4`:True and
`3\:>\:-1`: True

Both inequalities are satisfied, hence (0,3) is a solution to the given system of inequality.

Ans:True

QUESTION 5

The given system of inequality is

`y\:>\:2x-3` and
`y\:<\:x+6`.

If (-3,0) is a solution; then it must satisfy both inequalities.

We put x=-3 and y=0 in to both inequalities.

`0\:>\:2(-3)-3` and
`0\:<\:-3+6`.

`0\:>\:-9`;True and
`0\:<\:3`:True

Both inequalities are satisfied, hence (-3,0) is a solution to the given system of inequality.

Ans:True