#### Question

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

2*x* + *y* = 35

3*x* + 4*y* = 65

#### Solution

The given system of equations may be written as

2*x* + *y* - 35 = 0

3*x* + 4*y* - 65 = 0

Here

`a_1 = 2, b_1 = 1, c_1 = -35`

`a_2 = 3, b_2 = 4, and c_2 = -65`

By cross multiplication, we have

`=> x/(1xx (-65) - (-35) xx 4) = (-y)/(2xx(-65)-(-35)xx3) = 1/(2xx4 - 1xx3)`

`=> x/(-65 + 140) = (-y)/(-130 + 105) = 1/(8 -3)`

`=> x/75 = (-y)/(-25) = 1/5`

`=> x/75 = y/25 = 1/5`

Now

`y/25 = 1/5`

`=> y = 25/5 =5`

Hence, x = 15, y = 5is 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 : 2x + Y = 35 3x + 4y = 65 Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method.