#### Question

Solve each of the following systems of equations by the method of cross-multiplication

2*x* − *y* = 6*x* − *y* = 2

#### Solution

The given system of equations may be written as

2*x* − *y* - 6 = 0*x* − *y* - 2 = 0

Here

`a_1 = 2, b_1 = -1, c_1 = -6`

`a_2 = 1, b_2 = -1, c _2 = -2`

By cross multiplication, we get

`=> x/((-1)xx(-2)-(-6)xx(-1)) = (-y)/(2xx(-2)-(-6)xx1)= 1/(2xx (-1) -( -1)xx1)`

`=> x/(2-6) = (-y)/(-4+6)= 1/(-2 + 1)`

`=> x/(-4) = (-y)/2 = 1/(-1)`

`=> x/(-4) = (-y)/2 = 1`

Now

`x/(-4) = -1`

`=> x = (-4) xx (-1) = 4`

And

`(-y)/2 = -1`

`=> (-y) = (-1) xx 2`

=> -y = -2

=> y = 2

Hence, x = 4, y = 2 is the solution of the given system of the equations

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#### APPEARS IN

Solution Solve Each of the Following Systems of Equations by the Method of Cross-multiplication 2x − Y = 6 X − Y = 2 Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method.