SOLUTION: Double the larger number plus three times the smaller number makes 19 the difference between the numbers is 2

Question 1022546: Double the larger number plus three times the smaller number makes 19 the difference between the numbers is 2
Found 2 solutions by fractalier, addingup:
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call the larger and smaller numbers x and y. Then we have
x - y = 2 and
2x + 3y = 19
Solve the first and substitute into the second...
x = y+2
so that
2(y+2) + 3y = 19
2y + 4 + 3y = 19
5y + 4 = 19
5y = 15
y = 3
so that
x = 5.
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
Double the larger number: 2x
plus three times the smaller number makes 19
2x+3y = 19 (1)
the difference between the numbers is 2
x-y = 2
Add y on both sides:
x = 2+y
Let's plug this value for x into (1) above:
2(2+y)+3y = 19
4+2y+3y = 19
Add y on left and subtract 4 on both sides
5y = 15
divide both sides by 5
y = 3
Now that we know y let's find x The problem says that x-y = 2:
x-3 = 2
Add 3 on both sides:
x = 5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check - The problem says:
2x+3y = 19
2(5)+3(3)= 19 Do the math on left to see that we have the correct answer.
J

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