Question

Given the system of equations:

1. 5a+3p+1c+49=0
2. 3a+2p+1c=35
3. 2a+p+2c=34

Solve for the value of 'p' in the system of equations above using the method of substitution or elimination. Please provide a step-by-step explanation of the process used to find the value of 'p'.

Answer 1

To find the value of 'p', we can use the method of elimination. By eliminating 'a' from the given system of equations and substituting the value of 'c', we can solve for 'p'. The value of 'p' is 67.

Step-by-step explanation:

We can solve for the value of 'p' in the given system of equations using the method of elimination. Let's start by eliminating the variable 'a' from equations (2) and (3). Multiply equation (3) by 3 and equation (2) by 2 to make the coefficients of 'a' the same:

1. 6a+3p+3c=102
2. 6a+4p+2c=70

Now, subtract equation (2) from equation (1) to eliminate 'a':

6a+3p+3c-(6a+4p+2c)=102-70

-p+c=32

We have eliminated 'a'. Next, substitute the value of 'p' from equation (3) into the above equation:

-(2a+p+2c)+c=32

-2a-2c+c=32

-2a-c=32

Finally, solve this equation for 'p':

-c=32+2a

c=-32-2a

Substitute the value of 'c' in equation (2) and solve for 'p':

3a+2p+1(-32-2a)=35

3a+2p-32-2a=35

p=35+32

p=67