Question

solve for x and y 2x+y=7,4x-3y+1=0

Answer 1

2x+y=7-----(1) and 4x-3y+1=0
⇒4x-3y=-1---(2)
Adding (1) and (2),
  2x+y=7
+ 4x-3y=-1
⇒6x-2y=6
⇒2(3x-y)=6
⇒3x-y=3-----(3)
Adding (1) and (3),
  2x+y=7
+3x-y=3
⇒5x=10
⇒x=10/5
⇒x=2
Substituting 'x' in (1),
2(2)+y=7
⇒4+y=7
⇒y=7-4
⇒y=3

Answer 2

2x + y = 7              equation [1] 
4x - 3y + 1 = 0  or    4x - 3y = -1              equation [2]

Multiply eq [1] by 2 and eq [2] by 1 we get, 

4x + 2y = 14 
4x - 3y = -1 
___________ 
 2y + 3y = 14 + 1 
 ⇒5y = 15 
⇒ y = 15/5 
 ⇒y = 3 

Putting the value of y in eq [1] we get, 

2x + y = 7 
⇒ 2x + 3 = 7 (since y = 3) 
⇒2x = 7 - 3 
⇒ 2x = 4 
⇒ x = 4/2 
⇒ x = 2 

Answer
x = 2 
y = 3