1

Problem

If there is no solution of the linear equation system 4x + 5y = 5, 2x + ky = 9, then find the value of k?

2

Step

Consider the two linear equations are

\$ a_1x + b_1x = c_1 \$…​…​.equation (1)

\$ a_2x + b_2x = c_2 \$…​…​.equation (2)

3

Hint

If equation(1) and equation (2) have no solution then we can write: \$ (a_1)/(a_2) = (b_1)/(b_2) ne (c_1)/(c_2) \$ …​…​.equation (3).

4

Step

First, we will compare 4x + 5y = 5 with equation (1) and 2x + ky = 9 with equation (2). So by comparing the coefficients, we can write:

\$a_1 = 4, a_2 = 2, b_1 = 5, b_2 = k, c_1 = 5, c_2 = 9\$

5

Step

Now substitute the values in equation (3) then simplify:

\$ 4/2 = 5/k ne 5/9 \$ …​…​.equation(3)

\$ 4/2 = 5/k \$

\$ 4k = 10 \$

6

Step

Solve for k value:

\$ (\cancel(4^1)k)/(\cancel4^1) = (\cancel10^5)/(\cancel4^2) \$

\$ k = 5/2 \$

7

Solution

Therefore, the value of k is \$ 5/2\$.

8

Sumup

Please summarize steps

Choices

9

Choice-A

This option is wrong: It represents the inverse of the correct value for k

Wrong \$ k = 2/5\$

10

Choice-B

This option is wrong: It represents the negative value but the k is the positive value

Wrong \$ k = -5/2\$

11

Choice-C

This option is wrong: It represents the inverse of the correct value for k and sign is negative

Wrong \$ k = -2/5\$

12

Choice-D

This option is correct: It represents the correct value by using the formula

Correct \$ k = 5/2\$

13

Answer

Option

D

14

Sumup

Please summarize choices