Question

Solve the following system algebraically, for values a, b, and c.

2a + b + c = 17

1/2c = 5

a-b=5

Answer 1

a= 4

b= -1

c= 10

Explanation:

First we start by multiplying both sides of 1/2c = 5 by 2.

c = 10

Add b to both sides of the last equation to make it a=b+5

knowing these two things, we can plug them into the first equation like this:

2(b+5) + b + 10 = 17

then you solve for b:

distribute the 2

2b + 10 + b + 10 = 17

combine like terms

3b + 20 = 17

subtract 20 from each side

3b = -3

divide by 3

b = -1

then you can plug that into the last equation again so a - (-1) =5

Subtracting a negative is the same as adding so its a + 1 = 5 or a = 4