Question

How do you solve the following linear system: `4x+3y= -2 , 2x-2y= -8`?

Answer 1

(x , y) = ( -2 , 2 )

Explanation:

Let the given equations be
4x + 3y = -2 ..........(i)
2x - 2y = -8 ...........(ii)
Lets multiply equation (ii) by 2, we get
4x - 4y = -16 ..........(iii)
Subtract equation (iii) from (i)
4x + 3y = -2
4x - 4y = -16

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( - ) (+ ) (+)

0   + 7y = 14
 y = 14/7 = 2

Substituting value of y in equation (i)
4x + 3 X 2 = -2
or, 4x = -2 -6 = -8
or, x = -8/4 = -2
Hence (x , y) = ( -2 , 2 )
Checking
4 X -2 + 3 X 2 = -2
or, -8 + 6 + -2
or -2 = -2
Hence LHS = RHS