120k views
4 votes
To solve the system of equations below, Elena begins by multiplying the first equation by 5.

2x + 3y = 14
7x + 5y = 16

PART A
Elena wants to eliminate a variable by adding the equations together. By what integer could
Elena multiply the second equation?

PART B
Solve the system of equations algebraically. You may use Elena's strategy or one of your own.
Show your work.

User Beiller
by
8.1k points

1 Answer

4 votes

Answer:

x = -2

y = 6

Explanation:

Part A

If she multiplies the 1st equation by 5, then she should multiply the 2nd equation by -3. Then add the two results

(1) 2x + 3y = 14 (2) 7x + 5y = 16

10x + 15y = 70 -21x - 15y = -48

-21x - 15y = - 48

-11x = 22

x = - 2 7(-2) + 5y = 16

-14 + 5y = 16

5y = 30

y = 6

Check: Substitute values in (1) 2(-2) + 3(6) = -4 + 18 = 14 Yea! they work

User Roastbeeef
by
8.7k 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