The property of equality of the rows, columns, and diagonals in the magic
square can be used to find the value of <em>n</em>.
The value of <em>n</em> is 6
Reasons:
The magic square can be presented as follows;
![\begin{array}{|c|c|c|}n-2&3&n + 2\\n + 3&n - 1&1\\2&2 \cdot n - 5&n\end{array}\right]](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7B%7Cc%7Cc%7Cc%7C%7Dn-2%263%26n%20%2B%202%5C%5Cn%20%2B%203%26n%20-%201%261%5C%5C2%262%20%5Ccdot%20n%20-%205%26n%5Cend%7Barray%7D%5Cright%5D)
Given that the sum of the numbers in each row and in each column and in
each of the two diagonals are equal, to find the value of <em>n</em>, two rows having
different number of the variable <em>n</em> can be equated as follows;
The top row = n - 2 + 3 + n + 2 = The bottom row = 2 + 2·n - 5 + n
n - 2 + 3 + n + 2 = 2 + 2·n - 5 + n
2·n + 3 = 3·n - 3
3·n - 3 = 2·n + 3 (symmetric property)
3·n - 2·n = 3 + 3
n = 6
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Look at the first line in the first problem.
x y
<span>–6 –6
–4 –3</span>
find the slope:
y2-y1 / x2-x1
-3+6 / -4+6
3 / 2
the slope is 3/2. now plug this into point-slope form, along with one of the ordered pairs. i'll use (-4,-3) because the numbers are smaller.
y-y1=m(x-x1)
y+3=3/2(x+4)
y+3=3/2x+6
y=3/2x+3
now do the same for the other line.
<span>x y
0 3
2 6
actually, this one's convenient, because it tells you the y-intercept is 3 (when an ordered pair has a 0 as its x coordinate, that means its on the y axis). so we just have to find the slope.
y2-y1 / x2-x1
6-3 / 2-0
3/2
the line is y=3/2x+3. it's the same line as before. that means there are infinitely many solutions, because there are an infinite amount of points where the lines "cross" each other (since they lie on top of each other).
follow the same procedure for the next problem. if the equations turn out to be the same, it has infinite solutions. if the two lines have the same slope but different intercepts, that means they're parallel, and have no solution since the lines will never intersect. if the lines have different slopes, they will have one solution. and it makes no sense for lines to intersect at two different points, so you can ignore that option altogether.
hope this helps
</span>
No, it is not. This is because there is only one variable, instead of two.
