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  

$2x-y\:$ 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.

$2(0)-3\:$ and $0+3\:>\:-1$.

$-3\:$: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 $y\:$.

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 $0\:$.

$0\:>\:-9$;True and $0\:$:True

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

Ans:True