For which value(s) of k will the pair of equations kx + 3y = k - 3 and 12x + ky = k have no solution?

By Ritesh|Updated : November 8th, 2022

For k = -6, the pair of equations kx + 3y = k - 3 and 12x + ky = k have no solution. Steps to calculate the value of k will the pair of equations kx + 3y = k - 3 and 12x + ky = k:

Step 1: Equations should be changed to standard form.

a pair of linear equations are given,

kx + 3y = k - 3 and 12x + ky = k

the equations provided are transformed to standard form,

kx + 3y = k - 3 → kx + 3y + (3 - k) = 0

12x + ky = k → 12x + ky - k = 0

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.

Summary:

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.

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