SOLUTION: twice one number added to another number is 18. four times the first number minus the other number is 12. find the numbers.

Question 248822: twice one number added to another number is 18. four times the first number minus the other number is 12. find the numbers.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
The statements become the following equations.
2x + y = 18
4x - y = 12
.
2x + y = 18
Subtract 2x from both sides
y = -2x + 18
.
Substitute into the 2nd equation
4x - (-2x + 18) = 12
4x +2x - 18 = 12
Combine terms
6x -18 = 12
Add 18 to both sides
6x = 30
Divide both sides by 6
x = 5
.
Looking back, we recall:
2x + y = 18
4x - y = 12
.
2(5) + y = 18
10 + y = 18
Subtract 10 from both sides
y = 8
.
4(5)-8 = 12
True
.
So the two numbers are:
x = 5
y = 8
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