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

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2 Answers

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 :)
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!!