Answer:
Explanation:
AI-generated answer
To determine the value of k for which the system of equations has no solution, we need to examine the coefficients of x and y in the two equations. Let's solve the system step by step:
1. Given equations:
x + 2y = 5 (equation 1)
3x + ky - 15 = 0 (equation 2)
2. We can rewrite equation 2 in terms of x and y:
3x + ky - 15 = 0
ky = -3x + 15
y = (-3x + 15)/k
3. Now, let's substitute the value of y from equation 1 into equation 2:
x + 2((-3x + 15)/k) = 5
4. Simplify the equation:
x - 6x/k + 30/k = 5
5. Combine like terms:
(kx - 6x + 30)/k = 5
6. Multiply both sides of the equation by k to eliminate the fraction:
kx - 6x + 30 = 5k
7. Rearrange the equation:
kx - 6x = 5k - 30
(k - 6)x = 5k - 30
8. For the system to have no solution, the coefficients of x on both sides must be equal, but the constant terms must be different.
9. Setting the coefficients equal:
k - 6 = 0
10. Solve for k:
k = 6
Therefore, the system of equations has no solution when k = 6.