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The sum of two integers is 56 and their difference is 4. what are the two integers

User ACuria
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8.9k points

2 Answers

3 votes

Answer:


x+y=56,\:x-y=4\quad :\quad y=26,\:x=30

Explanation:


\star\star\star\star~\textrm{Let the two integers be x and y respectively.}~\star\star\star\star


\textrm{Then, our equations will look like;}


\begin{bmatrix}x+y=56\\ x-y=4\end{bmatrix}


\black{\mathrm{Isolate}\:x\:\mathrm{for}\:x+y=56:}


x+y=56


\gray{\mathrm{Subtract\:}y\mathrm{\:from\:both\:sides}}


x+y-y=56-y


\gray{\mathrm{Simplify}}


x=56-y


\gray{\mathrm{Subsititute\:}x=56-y}


\begin{bmatrix}56-y-y=4\end{bmatrix}


\black{\mathrm{Isolate}\:y\:\mathrm{for}\:56-y-y=4:}


56-y-y=4


\gray{\mathrm{Add\:similar\:elements:}\:-y-y=-2y}


56-2y=4


\gray{\mathrm{Subtract\:}56\mathrm{\:from\:both\:sides}}


56-2y-56=4-56


\gray{\mathrm{Simplify}}


-2y=-52


\gray{\mathrm{Divide\:both\:sides\:by\:}-2}


\displaystyle(-2y)/(-2)=(-52)/(-2)


\gray{\mathrm{Simplify}}


y=26


\gray{\mathrm{For\:}x=56-y}


\gray{\mathrm{Subsititute\:}y=26}


x=56-26


\gray{56-26=30}


x=30


\gray{\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}}


y=26,\:x=30


\blue{\mathrm{Plotting:}~x+y=56,\:x-y=4}

The sum of two integers is 56 and their difference is 4. what are the two integers-example-1
User Gijo Varghese
by
8.4k points
3 votes

Let
a,b\in\mathbb{Z} then we have a system of equations.

First the sum of a and b is 56.

a + b = 56

Second the difference of a and b is 4.

a - b = 4

From here our system of equations is,


a+b=56\wedge a-b=4

We can solve it using the elimination. If you add both of the equations the b terms cancel out hence,


2a=60\Longrightarrow a=30

Now that we have a value of a we can calculate b. Just pick one equation from the system.


30-b=4\Longrightarrow b=26

And the solutions to the system are two positive integers
\underline{a=30},\underline{b=26}

Hope this helps!

User Cjauvin
by
8.9k points

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