Question

1) 2x + y = 12 x + 2y = 9 Solve the following systems algebraically and check

Answer 1

Answer: x = 5, y = 2; Solution = (5, 2)

Step-by-step 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!