(Solved):   1. Solve the simultaneous equations using elimination: a. \( 5 x+3 y=41 \) \( 2 x+3 y=20 \ ...

 

1. Solve the simultaneous equations using elimination: a. \( 5 x+3 y=41 \) \( 2 x+3 y=20 \) b. \( 5 x+y=11 \) \( 3 x-y=9 \) 2. Solve the simultaneous equations using Substitution: a. \( x+7 y=64 \) \( x+3 y=28 \) b. \( 4 x-4 y=24 \) \( x-4 y=3 \) 3. Solve the simultaneous equations using Cramer's Rule: a. \( 2 x+4 y=14 \) \( 4 x-4 y=4 \) b. \( 2 x+4 y=26 \) \( 3 x-y=4 \) 4. David Buys 2 DVDs and 2 CDs in a shop with 18 USD Ellie Buys 3 DVDs and 2 CDs in the same shop and they cost 22 USD Form two equations and solve to find the cost of each \( \mathrm{CD} \) and DVD 5. Solve the following using Cramer's Rule a. \( 2 x+5 y+2 z=-38 \) \( 3 x-2 y+4 z=17 \) \( -6 x+y-7 z=-12 \) b. \( 3 x-9 z=33 \) \( 7 x-4 y-z=-15 \) \( 4 x+6 y+5 z=-6 \) 6. For the following equations, find i. Matrix \( \mathrm{A} \) if \( A X=B \), ii. Find \( A^{-1} \), iii. Find the value of \( \mathrm{x} \) and \( \mathrm{y} \) : a. \( 2 x+4 y=14 \) \( 4 x-4 y=4 \) b. \( 6 x+y=18 \) \( 4 x+y=14 \) c. \( 3 x+2 y=8 \) \( 2 x+5 y=-2 \) 7. Calculate: a. \( \sum_{i=0}^{10}(3 i-1) \) b. \( \sum_{i=0}^{20}(4 i+7) \) c. \( \sum_{i=0}^{15}(5 i+3) \) d. \( \sum_{i=0}^{25}\left(3 i^{2}+i-2\right) \)