Answer: x = 5, y = 2; Solution = (5, 2)
Explanation:
Substitution
2x + y = 12
x + 2y = 9
x + 2y = 9
Subtract 2y from both sides
x = 9 - 2y
Now, substitute x for (9 - 2y) in the first equation
2x + y = 12
2 (9 - 2y) + y = 12
Distribute 2
18 - 4y + y = 12
18 - 3y = 12
Subtract 18 from both sides
-3y = -6
Divide both sides by -3
y = 2
Now to find x, substitute 2 for y in (x = 9 - 2y)
x = 9 - 2y
x = 9 - 2(2)
x = 9 - 4
x = 5
Solution: (5, 2)
Elimination
2x + y = 12
x + 2y = 9
Multiply the second equation by -2 to find y
2x + y = 12
(x + 2y = 9) -2
2x + y = 12
-2x - 4y = -18
Add both equations
2x and -2x are cancelled out
You get:
-3y = -6
Divide both sides by -3
y = 2
Substitute 2 for y in any of the equations to find x
I chose x + 2y = 9
x + 2y = 9
x + 2 (2) = 9
x + 4 = 9
Subtract both sides by 4
x = 5
Solution = (5, 2)
Btw you can use any of these methods, I used both so you could know that you get the same answer no matter the method.
Hope I helped!