Suppose that kristen ate five hamburgers and drank two medium sodas, for a total of 1790 calories. kristen friend back ate two hamburgers and drank three medium sodas, for a total of 1178 calories. how many calories are in a hamburger? how many calories are in a soda? me

If H and S represent the calorie content of hamburgers and sodas, respectively, then you have
.. 5H +2S = 1790
.. 2H +3S = 1178

By Cramer's rule, (Google it)
.. H = (2*1178 -3*1790)/(2*2 -3*5) = -3014/-11 = 274
.. S = (1790*2 -1178*5)/-11 = -2310/-11 = 210

There are 274 calories in a hamburger; 210 calories in a soda.

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Actually, the above solution is found using the methods of Vedic mathematics. The formula for
.. ax +by =c
.. dx +ey = f
is
.. x = (bf -ec)/(bd -ae) . . . . . . . the products are a simple crossing pattern
.. y = (cd -fa)/(same denominator)

The actual Cramer's Rule uses the negative of both numerator and denominator, that is (ce-bf)/(ae-bd) = x, for example. I find the Vedic pattern of products easier to remember.

As with most math problems, there are many ways to solve it. You are probably taught methods of elimination and substitution. Graphing works, too. (See the image.)