Six times a larger number is equal to the sum of a smaller number and 18. The difference of twice the larger number and the smaller number is 6. Let x represent the smaller number and y represent the larger number. Which equations represent the situation?

6 times a larger number (so 6y) is equal (=) to the sum of a smaller number and 18 (x+18)

6y = x+18

Twice of larger number (2y) and the difference of smaller number (x) is equal to 6

2y - x = 6

solve for y. Divide both terms for 6.

6y/6 = 1/6x+3

y = 1/6x+3

second equation solve for y

move x to the right of equal

2y = x + 6

y = 1/2x + 3

ANSWER D!

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Palky Palky · Answer 2 · 2022-01-18T12:12:21+01:00

y = x / 6 + 3 and y = x / 2 + 3 are the equations, with solution x = 0 & y = 6

Given : Smaller and larger numbers are denoted by x & y.

Six times a larger number is equal to the sum of a smaller number and 18, implies 6y = x + 18 (i)

Dividing LHS & RHS of equation i) by 6,

y = x / 6 + 3

The difference of twice the larger number and the smaller number is 6, implies 2y - x = 6 ; 2y = x + 6 (ii)

Dividing LHS & RHS of equation ii) by 2,

y = x / 2 + 3

Solving these equations :

Getting the value of x from equation ii),

x = 2y - 6

Putting the value of y in equation i),

6y = 2y - 6 + 18

6y - 4y = 18 - 12

2y = 6

y = 6/2 = 3

Putting the value of x in y ,

x = 2 (3) - 6 = 6 - 6 = 0

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