David W. answered • 07/04/17
Tutor
4.7
(90)
Experienced Prof
Let:
x = smaller integer
y = greater integer
Translate:
"greater of two integers is 7 more than twice the smaller" means
y = 7 + 2 * x [eq1]
"sum of the two integers is 37" means
x + y = 37 [eq2]
You may use substitution or elimination to solve for x and y. Let's find x, then substitute:
x = 37 - y [from eq2]
y = 7 + 2(37-y) [substitute for x]
y = 7 + 74 - 2y [distribute]
3y = 81 [add 2y to both sides]
y = 27 [divide both sides by 3]
Now, substitute for y in either equation [you should get the same result; let's use eq2]
x = 37 - 27
x = 10
Checking (very important):
Is 27 = 7 + 2(10) ?
27 = 27 ?yes
Is 10 + 27 = 37 ?
37 = 37 ?yes
David W.
Note that you may assign variables any way you want. But:
- assign them so that you can remember them (or review your "Let" statement)
- if possible, assign a variable to the result the problem asks you to find (so you don't forget to solve for it at the end)
- use the correct values when you check the equations
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07/05/17
Arturo O.
John,
x = 7 + 2y works too, as long as x is the larger number in this case. The system becomes
x - 2y = 7
x + y = 37
The solution is
x = 27
y = 10
You just exchanged x with y, so your approach was valid too.
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07/05/17
John E.
07/04/17