Question 1123099
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<pre>
25*b +  2*m = 29    grams of protein   (1)
11*b + 25*m = 61    grams of calcium   (2)


Multiply eq(1) by 25 (both sides);  multiply eq(2) by 2 (both sides). You will get


25*25*b + 50*m = 25*29    (3)
 2*11*b + 50*m =  2*61    (4)


Subtract eq(4) fro eq(3). You will get


25*25*b - 2*11*b = 25*29-2*61,   or


(25*25 - 2*11)*b = 25*29 - 2*61


b = {{{(25*29 - 2*61)/(25*25-2*11)}}} = 1.    (*)  <<<---=== I specially / (intently) did not make intermediate calculations until I got this formula.
                                      Then I copied the formula to Excel spreadsheet in my computer and calculated it "in one click".


Thus you just found "b" by elimination.


Now from eq(1),  m = {{{(29-25*1)/2}}} = 2.


<U>Answer</U>.  b= 1,  m= 2.
</pre>

Solved.


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If you just know the determinant method &nbsp;(which is the same as the &nbsp;Cramer's rule),
you will easily recognize that the denominator in the formula &nbsp;(*) &nbsp;is the determinant of the coefficient matrix 
to equations &nbsp;(1) &nbsp;and &nbsp;(2), &nbsp;while the numerator is the determinant of the modified matrix by the &nbsp;Cramer's rule.


When you use the Elimination method, &nbsp;it is an additional way to check that all your actions are / were correct.