Linear Equation
For what values of ‘k’ will the pair of equations 3x + 4y = 12 and kx + 12y = 30 NOT have a unique solution?For what values of ‘k’ will the pair of equations 3x + 4y = 12 and kx + 12y = 30 NOT have a unique solution?
someone please help me in solving the above question?
Hi Faiz,
For two pairs of equations to not have a solution, they must be parallel. Since two parallel lines have equal slopes, we can equate the slopes and find the value of k.
3x + 4y = 12 —–> 4y = -3x + 12 —–> y = (-3/4)x + 3 —–> m = -3/4
kx + 12y = 30 —–> 12y = -kx + 30 —–> y = (-k/12)x + 30/12 —-> m = -k/12
-3/4 = -k/12 —-> k = 9.
Hope this helps!
