Step 2: By comparing the equations to the reference formula.
Using the conventional form to compare the two equations, we define
a1 = k, b1 = 3, and c1 = 3 - k
a2 = 12, b2 = k, and c2 = -k
Step 3: Write the circumstances in which there are no solutions.
The supplied set of equations must meet the condition if there is no solution.
a2/a2 = b2/b2 ≠ c2/c2
k/12 = 3/k ≠ (3-k)/-k
Step 4: Obtain value for k
From the first two parts,
k/12 = 3/k
k2 - 36 = 0
k = ± 6
From the last two parts,
3/k ≠ (3-k)/-k
k - 3 ≠ 3
k ≠ 6
From the last two results, we know that for k = -6, the equations will have no solutions
Hence, for k = -6, the set of equations has no solutions.
For which value(s) of k will the pair of equations kx + 3y = k - 3 and 12x + ky = k have no solution?
For k = -6, the pair of equations kx + 3y = k - 3 and 12x + ky = k have no solution. The pair of equations has to be written in standard form and solved by comparison in order to obtain the k value.