The ordered pair (5,-3) is a solution to which of the following inequalities? ygeqslant -2x+8 y-2xgt 5 4y+2xleqslant -1 -2ylt 3x-9

## Step 1: Substitute the Ordered Pair into Each Inequality<br />### For each inequality, substitute \( x = 5 \) and \( y = -3 \) to check if the ordered pair satisfies the inequality.<br /><br />## Step 2: Check the First Inequality<br />### Substitute into \( y \geq -2x + 8 \):<br />\[<br />-3 \geq -2(5) + 8 \\<br />-3 \geq -10 + 8 \\<br />-3 \geq -2<br />\]<br />This is false.<br /><br />## Step 3: Check the Second Inequality<br />### Substitute into \( y - 2x > 5 \):<br />\[<br />-3 - 2(5) > 5 \\<br />-3 - 10 > 5 \\<br />-13 > 5<br />\]<br />This is false.<br /><br />## Step 4: Check the Third Inequality<br />### Substitute into \( 4y + 2x \leq -1 \):<br />\[<br />4(-3) + 2(5) \leq -1 \\<br />-12 + 10 \leq -1 \\<br />-2 \leq -1<br />\]<br />This is true.<br /><br />## Step 5: Check the Fourth Inequality<br />### Substitute into \( -2y < 3x - 9 \):<br />\[<br />-2(-3) < 3(5) - 9 \\<br />6 < 15 - 9 \\<br />6 < 6<br />\]<br />This is false.