Does the equation 7c+8p=29.60 help us to solve the original system? 5c+4p=18.40 2c+4p=11.20 If you think so, explain how it helps. If you don't think so, explain why not and what would help us solve the system.

According to the equation given 7c+8p=29.60, we will see that the two equation was added to get the required equation in question. Note that this equation 7c+8p=29.60 cannot help us to solve the simultaneous equation because the resulting equation is one equation with two unknown variables. For us to get a solution to the simultaneous equation, we need to reduce the system of equation to just an equation and a variable. This can be gotten by taking the difference of the two equation as shown: (Elimination method)

Equation 1 - equation 2 will give;

(5c-2c)+(4p-4p) = 18.40-11.20

3c+0 = 29.60

3c = 29.60

Divide both sides by 3

3c/3 = 29.60/3

c = 9.87

Substitute c = 9.87 into equation 2

From 2: 2c+4p = 11.20

c + 2p = 5.60

9.87 + 2p = 5.60

2p = 5.60 - 9.87

2p= -4.27

p = -4.27/2

p = -2.135

You can see that what helped in solving the system of equation is by eliminating one of the variables first using the Elimination method.