Which o inequantes ygt -3x+3 ygeqslant 2x-2 (1,0) (-1,1) (2,2) (0,3)

## Step 1: Analyze the first inequality $y > -3x + 3$<br />### Substitute each ordered pair into the inequality $y > -3x + 3$ and check if it holds true.<br />- For $(1, 0)$: Substitute $x = 1$ and $y = 0$. <br /> \[<br /> 0 > -3(1) + 3 \implies 0 > 0<br /> \]<br /> This is **false**. <br />- For $(-1, 1)$: Substitute $x = -1$ and $y = 1$. <br /> \[<br /> 1 > -3(-1) + 3 \implies 1 > 6<br /> \]<br /> This is **false**. <br />- For $(2, 2)$: Substitute $x = 2$ and $y = 2$. <br /> \[<br /> 2 > -3(2) + 3 \implies 2 > -3<br /> \]<br /> This is **true**. <br />- For $(0, 3)$: Substitute $x = 0$ and $y = 3$. <br /> \[<br /> 3 > -3(0) + 3 \implies 3 > 3<br /> \]<br /> This is **false**.<br /><br />### Only $(2, 2)$ satisfies the first inequality.<br /><br />## Step 2: Analyze the second inequality $y \geqslant 2x - 2$<br />### Substitute each ordered pair into the inequality $y \geqslant 2x - 2$ and check if it holds true.<br />- For $(1, 0)$: Substitute $x = 1$ and $y = 0$. <br /> \[<br /> 0 \geqslant 2(1) - 2 \implies 0 \geqslant 0<br /> \]<br /> This is **true**. <br />- For $(-1, 1)$: Substitute $x = -1$ and $y = 1$. <br /> \[<br /> 1 \geqslant 2(-1) - 2 \implies 1 \geqslant -4<br /> \]<br /> This is **true**. <br />- For $(2, 2)$: Substitute $x = 2$ and $y = 2$. <br /> \[<br /> 2 \geqslant 2(2) - 2 \implies 2 \geqslant 2<br /> \]<br /> This is **true**. <br />- For $(0, 3)$: Substitute $x = 0$ and $y = 3$. <br /> \[<br /> 3 \geqslant 2(0) - 2 \implies 3 \geqslant -2<br /> \]<br /> This is **true**.<br /><br />### The pairs $(1, 0)$, $(-1, 1)$, $(2, 2)$, and $(0, 3)$ satisfy the second inequality.<br /><br />## Step 3: Identify the ordered pairs that satisfy both inequalities<br />### Combine results from Steps 1 and 2:<br />- $(1, 0)$: Fails the first inequality. <br />- $(-1, 1)$: Fails the first inequality. <br />- $(2, 2)$: Satisfies both inequalities. <br />- $(0, 3)$: Fails the first inequality.<br /><br />### Only $(2, 2)$ satisfies both inequalities.