196k views
0 votes
1) 2x + y = 12
x + 2y = 9
Solve the following systems algebraically and check

User Pearpages
by
7.9k points

1 Answer

9 votes

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!

User Billyjoker
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories