Let [tex]a,b\in\mathbb{Z}[/tex] 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,
[tex]a+b=56\wedge a-b=4[/tex]
We can solve it using the elimination. If you add both of the equations the b terms cancel out hence,
[tex]2a=60\Longrightarrow a=30[/tex]
Now that we have a value of a we can calculate b. Just pick one equation from the system.
[tex]30-b=4\Longrightarrow b=26[/tex]
And the solutions to the system are two positive integers [tex]\underline{a=30},\underline{b=26}[/tex]
Hope this helps!
Answer:
[tex]x+y=56,\:x-y=4\quad :\quad y=26,\:x=30[/tex]
Step-by-step explanation:
[tex]\star\star\star\star~\textrm{Let the two integers be x and y respectively.}~\star\star\star\star[/tex]
[tex]\textrm{Then, our equations will look like;}[/tex]
[tex]\begin{bmatrix}x+y=56\\ x-y=4\end{bmatrix}[/tex]
[tex]\black{\mathrm{Isolate}\:x\:\mathrm{for}\:x+y=56:}[/tex]
[tex]x+y=56[/tex]
[tex]\gray{\mathrm{Subtract\:}y\mathrm{\:from\:both\:sides}}[/tex]
[tex]x+y-y=56-y[/tex]
[tex]\gray{\mathrm{Simplify}}[/tex]
[tex]x=56-y[/tex]
[tex]\gray{\mathrm{Subsititute\:}x=56-y}[/tex]
[tex]\begin{bmatrix}56-y-y=4\end{bmatrix}[/tex]
[tex]\black{\mathrm{Isolate}\:y\:\mathrm{for}\:56-y-y=4:}[/tex]
[tex]56-y-y=4[/tex]
[tex]\gray{\mathrm{Add\:similar\:elements:}\:-y-y=-2y}[/tex]
[tex]56-2y=4[/tex]
[tex]\gray{\mathrm{Subtract\:}56\mathrm{\:from\:both\:sides}}[/tex]
[tex]56-2y-56=4-56[/tex]
[tex]\gray{\mathrm{Simplify}}[/tex]
[tex]-2y=-52[/tex]
[tex]\gray{\mathrm{Divide\:both\:sides\:by\:}-2}[/tex]
[tex]\displaystyle\frac{-2y}{-2}=\frac{-52}{-2}[/tex]
[tex]\gray{\mathrm{Simplify}}[/tex]
[tex]y=26[/tex]
[tex]\gray{\mathrm{For\:}x=56-y}[/tex]
[tex]\gray{\mathrm{Subsititute\:}y=26}[/tex]
[tex]x=56-26[/tex]
[tex]\gray{56-26=30}[/tex]
[tex]x=30[/tex]
[tex]\gray{\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}}[/tex]
[tex]y=26,\:x=30[/tex]
[tex]\blue{\mathrm{Plotting:}~x+y=56,\:x-y=4}[/tex]
