2x+5y=7 3x+6y=3

Question

Use elimination to solve the system of equations. 2x+5y=7 

3x+6y=3

Answer 1

Hey Sydney -- "noticing offsets" ... an extra x+y drops the 7 to 3 ... x+y = -4 ...

 

double and subtract from 2x +5y =7 ... 3y = 15 ... y=5, x= -9 ... (-9,5) solves ... Regards :)

Answer 2

1. 2x + 5y = 7

2. 3x + 6y = 3

 

Multiply Equation 1. by -3 and Equation 2. by 2:

 

1'.  -6x - 15y = -21

2'.  6x + 12y = 6

 

Add Equations 1' and 2' to eliminate x

 

y(-15 + 12) = (-21 + 6)

 

-3y = -15

 

y = 5

 

Substitute this value of y into either Equation 1 or 2 and solve for x:

 

1. 2x + 5y = 7 ⇒ 2x + 5(5) = 7

 

2x = (7 - 25) = -18

 

x = -9

 

Check answer:

 

Does 3(-9) + 6(5) = 3?

 

Does -27 + 30 = 3?

 

YES!!