Question

for what the value of k,will the following pair of equation have infinitely many solution 2x+3y=7 and (k+2)x-3(1-k)y=5k+1

Answer 1

if they are coincide then we get many solution

we use any two ratios

2:3:7=k+2:3k-3:5k+1

2/3=(k+2)/(3k-3)

2(3k-3)=3(k+2)

6k-6=3k +6

6k-3k =6+6

3k=12

k=4

we can use another ratio also