Question

2kx + (k-1)y = 1, 3x - 5y =7. condition for no solution n find k.​

Answer 1

Answer:

Step-by-step explanation:

Let's solve for k. ( Equation 1)

2kx+(k−1)(y)=1

Step 1: Add y to both sides.

2kx+ky−y+y=1+y

2kx+ky=y+1

Step 2: Factor out variable k.

k(2x+y)=y+1

Step 3: Divide both sides by 2x+y.

k(2x+y) /2x+y   = y+1 /2x+y

k= y+1 /2x+y

Let's solve for x. (Equation 1)

2kx+(k−1)(y)=1

Step 1: Add -ky to both sides.

2kx+ky−y+−ky=1+−ky

2kx−y=−ky+1

Step 2: Add y to both sides.

2kx−y+y=−ky+1+y

2kx=−ky+y+1

Step 3: Divide both sides by 2k.

2kx /2k = −ky+y+1 /2k

x= −ky+y+1 /2k

Let's solve for x (Equation 2 )

3x−5y=7

Step 1: Add 5y to both sides.

3x−5y+5y=7+5y

3x=5y+7

Step 2: Divide both sides by 3.

3x /3 = 5y+7 /3

x= 5y /3 + 7 /3

Let's solve for y ( Equation 1)

2kx+(k−1)(y)=1

Step 1: Add -2kx to both sides.

2kx+ky−y+−2kx=1+−2kx

ky−y=−2kx+1

Step 2: Factor out variable y.

y(k−1)=−2kx+1

Step 3: Divide both sides by k-1.

y(k−1) /k−1 = −2kx+1 /k−1

y= −2kx+1 /k−1

Let's solve for y (Equation 2)

3x−5y=7

Step 1: Add -3x to both sides.

3x−5y+−3x=7+−3x

−5y=−3x+7

Step 2: Divide both sides by -5.

−5y /−5 = −3x+7 /−5

y= 3 x/5 + −7 /5