Question

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6) Practice: Organizing Information
Answer the questions and complete the steps to solve the system of equations below.
3x+2y=12
6x+3y=21

1.How can you get equal coefficients for the x-terms?


2. Multiply the top equation by 2.


3.Subtract the bottom equation from the new top equation. Show your work.





4. Use substitution to solve the system for x. Show your work.





5. Write your solution as an ordered pair (x, y).

6. Use substitution to check your solution for the system. Show your work.

Answer 1

ANSWERS

Question 1: By multiplying the first or top equation by 2

Question 2:

`2(3x+2y=12)\\\\=[2(3x)+2(2y)=2(12)]\\\\=6x+4y=24`

Question 3:

Subtract each like term;

[6x + 4y = 24]

- [6x + 3y = 21]

__________

[ 0 + y = 3 ] so, y = 3

Question 4:

Use the equation, 3x + 2y = 12 and substitute y =3:

`3x + 2(3) = 12\\3x + 6 = 12\\3x + 6 - 6 = 12 - 6\\3x = 6\\3x / 3 = 6 / 3\\\\x = 2`

Question 5:

An ordered pair is (x, y) so (2, 3)

Question 6:

So we check our answer but substituting x = 2 and y = 3, in 6x + 3y =21,

`6x +3y=21\\6(2)+3(3)=21\\12+9=21\\21=21`