# Solve the simultaneous equation: 2w - v = 5 w - 3v = 10

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The set of linear equations

2w - v = 5 ...(1)

w - 3v = 10 ...(2)

has to be solved for v and w.

From (1), we get v = 2w - 5, substitute this for v in (2)

=> w - 3(2w - 5) = 10

=> w - 6w + 15 = 10

=> -5w = -5

=> w = 1

As v = 2x - 5, v = -3

**The solution of the given set of equations is v = -3 and w = 1**

2w - v = 5 ---(1)

w - 3v =10 ---(2)

First we multiply (2) equation by 2 { (2)x 2 }

2w - 6v =20 ---(3)

then,

(1) subtract (3) { (1)-(2) }

(2w - v) - (2w - 6v) = 5 - 20

2w - v - 2w + 6v = -15

5v = -15

v = -3

Now apply v = -3 in (1)

2w - v = 5

2w - (-3) = 5

2w + 3 = 5

2w = 5-3

2w = 2

w= 1

Answers

w=1 , v =-3