# Solve the following system again using the addition method. Multiply the appropriate equation by the appropriate factor to eliminate p, and solve for c first. c+p=30 47c+44p=1350

Question
Systems of equations
Solve the following system again using the addition method. Multiply the appropriate equation by the appropriate factor to eliminate p, and solve for c first.
c+p=30
47c+44p=1350

2020-10-27
To use the addition method, one of the variables in both equations must have opposite coefficients. Since the coefficient of p in the second equation is 44, the coefficient of p in the first equation must be −44 to use the addition method. Multiplying both sides of c+p=30 by −44 gives −44c−44p=−1320. Add this to the second equation to eliminate pp. Then solve for c: -44c-44p=-1320
47c+44p=1350
3c=30
c=10
Substitute c=10 into c+p=30 and solve for p:
c+p=30
10+p=30
p=20
The solution of the system is then (c,p)=(10,20)

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