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# Solve Each of the Following Systems of Equations by the Method of Cross-multiplication : 2x + Y = 35 3x + 4y = 65 - CBSE Class 10 - Mathematics

ConceptAlgebraic Methods of Solving a Pair of Linear Equations Cross - Multiplication Method

#### Question

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

2x + y = 35
3x + 4y = 65

#### Solution

The given system of equations may be written as

2x + y - 35 = 0

3x + 4y - 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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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.
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