Question

Solve the following pair of linear equations by the substitution and cross-multiplication methods:
8x + 5y = 9
3x + 2y = 4​

Answer 1

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Answer 2

$\huge\underline\mathrm{SOLUTION:-}$

◼️8x + 5y = 9 …………………..(1)

◼️3x + 2y = 4 ……………….….(2)

From equation (2) we get:

◼️x = 4 - 2y / 3 ……………………. (3)

Using this value in equation 1, we get:

➠ 8(4 - 2y)/3 + 5y = 9

➠ 32 - 16y + 15y = 27

➠ -y = -5

◼️y = 5 ……………………………….(4)

Using this value in equation (2), we get:

➠ 3x + 10 = 4

➠ x = -2

• Thus, x = -2 and y = 5.

Now, Using Cross Multiplication method:

➠ 8x + 5y - 9 = 0

➠ 3x + 2y - 4 = 0

➠ x/(-20 + 18)

➠ y/(-27 + 32 )

➠ 1/(16-15)

➠ -x/2 = y/5 = 1/1

ThereFore:

• x = -2 and y =5

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