SOLUTION: A KELLY BOUGHT 2 TACOS AND 3 ENCHILLADAS. FRED BOUGHT 3 TACOS AND 5 ENCHILLADAS. ONE BILL IS $7.80 THE OTHER IS $12.70. HOW MUCH WAS EACH TACO AND ECHILLADA ?

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Question 124262: A KELLY BOUGHT 2 TACOS AND 3 ENCHILLADAS. FRED BOUGHT 3 TACOS AND 5 ENCHILLADAS. ONE BILL IS $7.80 THE OTHER IS $12.70. HOW MUCH WAS EACH TACO AND ECHILLADA ?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
2t+3e=7.8
3t+5e=12.7
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tacos cost $.90 and enchaladas $2.00
Ed
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Solved by pluggable solver: Linear Systems by Addition
We'll solve the system:
2%2At+%2B+3%2Ae+=+7.8
3%2At+%2B+5%2Ae+=+12.7
by elimination by addition.To eliminate by addition, we need to set both coefficients of x to numbers with changed signs, i.e a and -a. Since in the second equation we have 3 as our coefficient for x, to get -2 we have to multiply all terms of the second equation by -2%2F3 which is equal to -0.666666666666667.

Multiplying, we get on our second equation:%283%2A-0.666666666666667%29t+%2B+%285%2A-0.666666666666667%29e+=+12.7%2A-0.666666666666667
-2%2At+%2B+-3.33333333333333%2Ae+=+-8.46666666666667

Adding both equations we get:

%282%2B-2%29t+%2B+%283%2B-3.33333333333333%29e+=+%287.8%2B-8.46666666666667%29

Since 2 and -2 cancel out, we have a linear equation:Therefore, we know that e = 2.

Plugging that in into the first equation gives us:

2%2At+%2B+3%2Ae+=+7.8
2%2At+%2B+3%2A2+=+7.8
2%2At+%2B+5.99999999999999+=+7.8
2%2At+=+7.8+-+5.99999999999999
t+=+%287.8+-+5.99999999999999%29%2F2
t+=+1.80000000000001%2F2
t+=+0.900000000000004

Therefore, our answer is:

system%28+t=0.900000000000004%2C+e=2+%29