Solve the following system?

Question

a-2b=2
a+b=2(b+3)

Answer 1

a - 2b = 2
a + b = 2(b + 3)

Use substitution. Since a - 2b = 2, then a = 2 + 2b. Plugging this into the second equation,

2 + 2b + b = 2(b + 3)

Simplify and solve for b.

2 + 3b = 2b + 6
b = 4

Now that we have b, we can get a easily, since a = 2b + 2.
a = 2(4) + 2 = 8 + 2 = 10

a = 10, b = 4

Answer 2

a-2b=2
a+b=2(b+3) Subtract the first equation from this one.
3b=2(b+3)-2
3b=2b+6-2
b=4 Substitute 4 for b in the first equation.
a-8=2
a=10

Check
10-8=2 Yes.
10+4=2(4+3)
14=14 Yes.

Answer 3

a-2b=2
a+b=2b+6

a-2b=2
a-b=6

a-2b=2
-2a+2b=-12
=========
-a=-10
a=10

10-2b=2
-2b=-8
b=4

The solution set is (10,4)

Check:
10-2(4)=2
10-8=2
2=2

10+4=2(4+3)
14=14

I hope this helps!