Final answer:
To solve the system of equations -3C + 4D = 5 and C + 5D = 2, use the method of substitution. The solution is C = -7/19 and D = 11/19.
Step-by-step explanation:
To solve the given system of equations, we will use the method of substitution.
From the second equation, we can express C in terms of D as C = 2 - 5D.
Substituting this value of C into the first equation, we get -3(2 - 5D) + 4D = 5.
Simplifying this equation gives us -6 + 15D + 4D = 5.
Combining like terms, we have 19D = 11.
Dividing both sides by 19, we get D = 11/19.
Now substitute this value of D back into the second equation to find C. C + 5(11/19) = 2.
Simplifying this equation gives us C = 2 - 55/19 = -7/19.
Therefore, the solution to the system of equations is C = -7/19 and D = 11/19.