Please help me !! Give the best answer and explanation !!
Solve each story problem using a system of equations – remember to multiply one of your equations in order to get an inverse to cancel:
1) The sum of triple a number (x) and 9 times another number (y) equals -12. Twice that number (x) decreased by the product of 9 and other number (y) equals 22.
Find the two number .
Write your 2 equation using the variable "x" and "y" :
solve the system :
The value of x = _______ and the value of y = _______
2) The sum of twice a number (x) and 8 time another number (y) is equal to 48. Triple the number (x) decreased by the product of 8 and the other number (y) is equal to -68.
Write your two equations using the variable x and y :
Solve the system :
The value of x = _______ and the value of y = _______
3) Let snow resort offers two winter special : the getAway special and the extended stay special. The get-Away special offers two nights of lodging (N) and four meals (M) for $270. The Extended stay special offers three nights of lodging (N) and eight meals (M) for $435. Determine the cost of a night of lodging and the cost of a meal :
Write your 2 equation using "N" and "M" :
Solve your system :
The cost of a night is ________________
The cost of a meal is ________________
Answers
Answer :-
1) The sum of triple of x and 9 times y equals -12.
⇒ 3x + 9y = -12ㅤㅤㅤㅤㅤㅤㅤㅤ ( i )
Twice the number x decreased by the product of 9 and y equals 22.
⇒ 2x - 9y = 22 ㅤㅤㅤㅤㅤㅤㅤㅤ( ii )
Adding equation i and ii :-
⇒ 3x + 9y + 2x - 9y = 22 - 12
⇒ 5x = 10
⇒ x = 10 / 5
⇒ x = 2
Substituting the value in equation i :-
⇒ 3x + 9y = -12
⇒ 3 × 2 + 9y = -12
⇒ 9y + 6 = -12
⇒ 9y = -18
⇒ y = -18 / 9
⇒ y = -2
Value of x = 2
Value of y = -2
2) ) The sum of twice x and 8 times y is equal to 48.
⇒ 2x + 8y = 48 ㅤㅤㅤㅤㅤㅤㅤㅤ ( i )
Triple of x decreased by the product of 8 and y is equal to -68.
⇒ 3x - 8y = -68ㅤㅤㅤㅤㅤㅤㅤㅤ ( ii )
Adding the equation i and ii :-
⇒ 2x + 8y + 3x - 8y = 48 - 68
⇒ 5x = - 20
⇒ x = -20 / 5
⇒ x = -4
Substituting the value in equation i :-
⇒ 2x + 8y = 48
⇒ 2 × (-4) + 8y = 48
⇒ 8y - 8 = 48
⇒ 8y = 56
⇒ y = 56 / 8
⇒ y = 7
Value of x = -4
Value of y = 7
3) The get-Away special offers two nights of lodging (N) and four meals (M) for $270.
⇒ 2N + 4M = 270 ㅤㅤㅤㅤㅤㅤㅤㅤ ( i )
The Extended stay special offers three nights of lodging (N) and eight meals (M) for $ 435.
⇒ 3N + 8M = 435 ㅤㅤㅤㅤㅤㅤㅤㅤ ( ii )
Multiplying the equation i by 2 :-
⇒ 2 ( 2N + 4M = 270 )
⇒ 4N + 8M = 540 ㅤㅤㅤㅤㅤㅤㅤㅤ ( iii )
Subtracting equation ii from iii :-
⇒ 4N + 8M - 3N - 8M = 540 - 435
⇒ N = 105
Substituting the value in equation i :-
⇒ 2N + 4M = 270
⇒ 2 × 105 + 4M = 270
⇒ 4M + 210 = 270
⇒ 4M = 60
⇒ M = 60 / 4
⇒ M = 15