Question

Solve the following pairs of linear
equations by all the method :
Substitutione, elemination, Cross-multiplication and Reducing mothed.
x/y+y/15=4. x/3-y/12=19/4​

Answer 1

Answer:

Step-by-step explanation:

CROSS - MULTIPLICATION METHOD:

The general form of a pair of linear equations,

a1x + b1y + c1 = 0 , & a2x + b2y + c2 = 0.

When a1 / a2 ≠ b1 / b2, the pair of linear equations will have a unique solution.

To solve this pair of equations for x and y using cross-multiplication, we’ll arrange the variables x and y and their coefficients a1, a2, b1 and b2, and the constants c1 and c2 as shown below,

⇒ x = b1 c2 - b2 c1 / a1 b2 - a2 b1,

⇒ y = c1 a2 - c2 a1 / a1 b2 - a2 b1,

The above equation is generally written as :

x/ b1 c2 - b2 c1 = y/ c1 a2 - c2 a1 = 1/a1 b2 - a2 b1.

Substitution and elimination method:

given,

x / 6 + y / 15 = 4,

so now ,

1 / 3 ( x / 2 + y / 5 ) = 4,

x / 2 + y / 5 = 12 ------eq(1),

and given,

x / 3 - y / 12 = 19 / 4,

1/ 3 (x / 1 - y / 4 ) = 19 / 4,

x - y / 4 = 57 / 4 -----(2),

now multiply eq(1) by 1 and eq(2) by 1 / 2, we get ,

x / 2+ y / 5 = 12-----(3),

x / 2 - y / 8= 57 / 8----(4),

______________ subtract eq(4) from eq(3), we get ,

y/ 5 + y / 8 = 12 - 57 / 8,

13 y / 40 = 39 / 8,

y = 39 × 40 / 13 ×8,

y = 3× 5 = 15,

y = 15,

now put value of "y" in eq.(1), we get,

x / 2 + 15 / 5 = 12,

x = 9 ×2 = 18,

x = 18,

hence value of x =18 , and y = 15.

Hope it helps.