1. **Solve the simultaneous equations:** Given: $$10q + 2r = 70$$ $$10q + 8r = 130$$ 2. Subtract the first equation from the second to eliminate $q$: $$ (10q + 8r) - (10q + 2r) = 130 - 70 $$ $$ 10q - 10q + 8r - 2r = 60 $$ $$ 6r = 60 $$ 3. Solve for $r$: $$ r = \frac{60}{6} = 10 $$ 4. Substitute $r=10$ into the first equation: $$ 10q + 2(10) = 70 $$ $$ 10q + 20 = 70 $$ $$ 10q = 50 $$ $$ q = 5 $$ --- 5. **Solve the inequality:** $$ 8 + \frac{u}{4} \leq 12 $$ 6. Subtract 8 from both sides: $$ \frac{u}{4} \leq 4 $$ 7. Multiply both sides by 4: $$ u \leq 16 $$ --- 8. **Cinema ticket problem:** Let $a$ = cost of one adult ticket, $c$ = cost of one child ticket. Given: $$ 2a + 2c = 36 $$ $$ 2a + 5c = 57 $$ 9. Subtract the first equation from the second: $$ (2a + 5c) - (2a + 2c) = 57 - 36 $$ $$ 3c = 21 $$ $$ c = 7 $$ 10. Substitute $c=7$ into the first equation: $$ 2a + 2(7) = 36 $$ $$ 2a + 14 = 36 $$ $$ 2a = 22 $$ $$ a = 11 $$ 11. Calculate costs: (a) $6a + 6c = 6(11) + 6(7) = 66 + 42 = 108$ (b) $4a + 7c = 4(11) + 7(7) = 44 + 49 = 93$ (c) $3c = 3(7) = 21$ --- 12. **Number line for $x \leq -6$:** The correct number line is D: closed circle at $-6$ with arrow pointing left. --- 13. **Solve inequality:** $$ 6 > 2x $$ 14. Divide both sides by 2: $$ 3 > x $$ or equivalently $$ x < 3 $$ --- **Final answers:** - $q=5$, $r=10$ - $u \leq 16$ - (a) 108, (b) 93, (c) 21 - Number line D - $x < 3$