Question

solve the following pair of linear equations by the substitution and cross-multiplication method. 8x+5y=9....3x+2y=4​

Answer 1

Answer:

8x + 5y = 9. 3x + 2y = 4. So, the solution of the given pair of linear equations is x = -2,y = 5. Hence, the required solution of the given pair of linear equations is x = -2, y - 5.

Explanation:

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Answer 2

Solution using substitution method:

Given equations

8x + 5y = 9……….. ( i )

3x + 2y = 4…........ ( ii )

Simplifying eq 1

→ 8x + 5y = 9

→ x = ( 9 - 5y )/8......… ( iii )

Putting the value of x in eq ii

→ 3(9 - 5y)/8 + 2y = 4

→ 27 - 15y/8 + 2y = 4

→ (27 - 15y + 16y)/8 = 4

→ y = 32 - 27

→ y = 5

Putting the value of y in eq iii

→ x = [9 - 5(5)]/8

→ x = 9 - 25/8

→ x = - 2

.°. Hence, x = - 2 & y = 5

Solution using cross multiplication method:

8x + 5y = 9

8x + 5y - 9 = 0

3x + 2y = 3

3x + 2y - 3 = 0

By cross multiplication

8 \ / 5 \ / -9 \ / 8

\ / \ / \ /

\ / \ / \ /

/ \ / \ / \

3 2 -4 3

x/(-20 + 18) = y/(-27 + 32) = 1/(-16 + 15)

x/ - 2 = y/5 = 1/1

x/-2 = 1

x = -2

______________

y/5 = 1

y = 5