Question

solve this question please

Answer 1

For a system of equation to have infinite many solutions, there graphs should intersect. Now if you have learnt about straight lines, what that means is the slope of the line (how steep the graph is?) and the y intercept( where it cuts the y axis?) should be equal.

Now another way of saying that is for two equations

a1 x+ b1 y = c1 and

a2x + b2y =c2

if these two equations have infinite solutions, the $\frac{a1}{a2} =\frac{b1}{b2}=\frac{c1}{c2}$

So according to question

4x+5y=7 and

(k+2)x + 10y =2k+2

(4/k+2) = (5/10) = 7/(2k+2)

now for infinite solution, there must be an x which satisfies both conditions simultaneously

(4/k+2) = 5/10

4*2=k+2

k=6.

now this will make one of the condition true

other one

(5/10) = 7/(2k+2)

2k+2 = 14

2k=12

k=6.

Now both equation said they are okay until k=6, that is both will be satisfied, hence k=6 is your answer.

but if both equations gave different value of k, then your answer would have "There is no k such that both conditions is satisfied simultaneously".

Hope it helped