Question

3C+4D=5 2C+5D=2
solve for d and c

Answer 1

`C=(17)/(7), D=-(4)/(7)`

Step-by-step explanation:

The system of equation is the following:

`3C+4D=5\\2C+5D=2`

We can solve the system by expliciting C from the second equation. We get:

`2C+5D=2\\2C=2-5D\\C=(2-5D)/(2)=1-(5)/(2)D`

And if we know substitute C into the first equation, we find

`3C+4D=5\\3(1-(5)/(2)D)+4D=5\\3-(15)/(2)D+4D=5\\3-(15)/(2)D+(8)/(2)D=5\\3-(7)/(2)D=5\\-(7)/(2)D=2\\-7D=4\\D=-(4)/(7)`

And by substituting D into the second equation, we find

`C=1-(5)/(2)D=1-(5)/(2)(-(4)/(7))=1+(10)/(7)\\C=(7)/(7)+(10)/(7)=(17)/(7)`