Question

The sum of 4 times a number and six times a number is 36. the difference of five times the second number and three times the first number is 49. find the numbers

Answer 1

-3 and 8

Explanation:

4x + 6y = 36

2x + 3y = 185

y - 3x = 49

-3x + 5y = 49

2x + 3y = 18

3-3x + 5y = 49

6x + 9y = 54

-6x + 10y = 98

19y = 152y = 152/19y = 82x + 3y = 182x + 3(8) = 182x + 24 = 182x = 18 - 242x = - 6x = -6/2x = -3

Answer 2

4x + 6y = 36...reduce........2x + 3y = 18
5y - 3x = 49...rearrange...-3x + 5y = 49

2x + 3y = 18 ...multiply by 3
-3x + 5y = 49 ..multiply by 2
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6x + 9y = 54 (result of multiplying by 3)
-6x + 10y = 98 (result of multiplying by 2)
--------------add
19y = 152
y = 152/19
y = 8

2x + 3y = 18
2x + 3(8) = 18
2x + 24 = 18
2x = 18 - 24
2x = - 6
x = -6/2
x = -3

first number is -3, second number is 8