{ x = 1 y = 4 Explanation: Take a look at your starting system of equations { 5 x + y = 9 10 x − 7 y = − 18 Notice that if you multiply the first equation by ( − 2 ) , and add the right-hand sides and the left-hand sides of the equations separately, you can eliminate the x -term. This will leave you with one equation with one unknown, y . { 5 x + y = 9 ∣ ⋅ ( − 2 ) 10 x − 7 y = − 18 { − 10 x − 2 y = − 18 10 x − 7 y = − 18
--------------------------------------------------- − 10 x − 2 y + 10 x − 7 y = − 18 + ( − 18 ) − 9 y = − 36 ⇒ y = ( − 36 ) ( − 9 ) = 4 Now use this value of y in one of the two original equations to find the value of x 5 x + ( 4 ) = 9 5 x = 5 ⇒ x = 5 5 = 1
To find all the arrangements of letters in a word where all the letters are different, we just need to calculate the factorial of the number of letters.
The word "grateful" has 8 different letters, so the number of arrangements of letters is:
8! = 8*7*6*5*4*3*2 = 40,320 different arrangements
Your answer is A) 34. A rectangle has four sides as you know. If you use 34 as your width, both sides for width would total 68. Then, same steps as before, accounting for both length sides by multiplying 68 by 2 and get you’d get 136. 68 (both width sides) + 136 (both length sides) would get your total of 204.