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.

x = -2

y = 6

Step-by-step 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

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40