Question

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.

Answer 1

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