Worksheet - General Solution to Systems of Linear Equations 1. Person 1 - Solve the following system of linear equations for 1:. ax+by=p cx+dy=q by doing the following. 0 Multiply the top equation by d. 0 Multiply the bottom equation by b 0 Add the two new equations. 0 Solve for a: Person 2 - Solve the following system of linear equations for y. ax+by=p cx+dy=q by doing the following. 0 Multiply the top equation by c. 0 Multiply the bottom equation by a 0 Add the two new equations. 0 Solve for y 2. Solve the following system of linear equations for 1:. ex+fy+gz=r hx+iy+jz=s kx+ly+mz=t by doing the following. 0 Multiply the top equation by j. 0 Multiply the middle equation by g 0 Add the two new equations to get equation (*). 0 Multiply the bottom equation by j. 0 Multiply the middle equation by m 0 Add the two new equations to get equation (**). o Solve the system of equations (*) and (**). Trigonometry Activity 8a - General Arithmetic & Geometric Series 1. Find the sum S = 1+ 3+ 5 + . . . + 11 + 13 = > (2n -1) by doing the following: n=1 . Copy down the series S in forwards order (meaning, as typed above). . Underneath this, write the series S in reverse (backwards) order. . Add the two lines by adding the pairs of numbers in each column. . Simplify the result. [Hint: Determine how many terms are being added together on the right hand side.] . Solve for S. 2. Consider the diagram below. . What part of the diagram represents the series S? . Explain how the diagram below represents the process completed in problem 1. 3. Find the sum S = 1+2+ . . . + (m -2) + (m -1) +m= > n using the same steps n= 1 as in problem 1. m 4. Find the sum S = d+2d+ . . . + (m - 1)d + md = > nd using the same steps as in n=1 problem 1.. 3 3 3 1 " _ . 5.F1ndthesum S_3++H'+E+32_Z(_) bydomgthefollowmg. c Find the common ratio r of the series. 0 Copy down the series in forwards order. a Underneath this, write the series 1' - S in forwards order, shifted once to the right. [Hint: This step sets up the next step for a lot of cancellation] o Subtract the two lines by subtracting the pairs of numbers in each column. a Solve for S. 6. Consider the diagram below. 0 What part of the diagram represents the serias S? 0 Explain how the diagram below represents the process completed in problem 5. 7. Find the sum 5' = ar+ar2+ - - - +arm_l +m'm 2 Ear" using the same steps as in n=1 problem 5. 8. Assume that 1