3.4 Reducible to Linear Form

Step 1

Let $u = 1/x$ and $v = 1/y$ .

Step 2

System becomes: $2u + 3v = 13$ (1) and $5u - 4v = -2$ (2).

Step 3

Eliminate $v$ : Multiply (1) by 4 and (2) by 3.

Step 4

$8u + 12v = 52$ and $15u - 12v = -6$ .

Step 5

Add equations: $23u = 46 \implies u = 2$ .

Step 6

Find $v$ : $2(2) + 3v = 13 \implies 3v = 9 \implies v = 3$ .

Step 7

Convert back: $x = 1/u = 1/2$ , $y = 1/v = 1/3$ .

Final Answer

x=1/2, y=1/3

Operation

Equation 1: a1x + b1y + c1 = 0

Select operation and enter coefficients.