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Solve Each of the Following Systems of Equations by the Method of Cross-multiplication 3x + 2y + 25 = 0 2x + Y + 10 = 0 - CBSE Class 10 - Mathematics

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Question

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

3x + 2y + 25 = 0
2x + y + 10 = 0

Solution

The given system of equation is

3x + 2y + 25 = 0
2x + y + 10 = 0

Here

`a_1 = 3, b_1 = 2, c_1 = 25`

`a_2 = 2, b_2 = 1, c_2 = 10`

By cross-multiplication, we have

`=> x/(2xx 10-25xx 1) = (-y)/(3xx 10- 25xx 2) = 1/(3xx1 - 2xx2)`

`=> x/(20-25) = (-y)/(30-50) =- 1/(3-4)`

`=> x/(-5) = (-y)/(-20) = 1/(-1)`

Now `x/(-5) = 1/(-1)`

`=> x = (-5)/(-1) = 5`

And 

`(-y)/(-20) = 1/(-1)`

`=> y/20 = 1`

=> y = -20

Hence, x =  5, y = 20 is the solution of the given system of equations.

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APPEARS IN

Solution Solve Each of the Following Systems of Equations by the Method of Cross-multiplication 3x + 2y + 25 = 0 2x + Y + 10 = 0 Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method.
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