1

Problem

If there is no solution of the linear equation system 3a - b = 2, ma + 4b = 8, then find the value of m?

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 3a - b = 2 with equation (1) and ma + 4b = 8 with equation (2). So by comparing the coefficients, we can write:

\$a_1 = 3, a_2 = m, b_1 = - 1, b_2 = 4, c_1 = 2, c_2 = 8\$

5

Step

Now plug the values in equation (3):

\$ 3/m = - 1/4 ne 2/8 \$ …​…​.equation (3)

6

Step

Now taking the first two parts of the above equation then simplify:

\$ 3/m = - 1/4 \$

7

Step

By using cross multiplication, and then simplify:

12 = - m

-12 = - (- m)

m = - 12

8

Solution

Therefore, the value of m is -12.

9

Sumup

Please summarize steps

Choices

10

Choice-A

This value would not make the coefficients of a and b proportional in the same manner as required for no solution

Wrong \$m = 1/(12)\$

11

Choice-B

After Inspecting the coefficients, we found that the value of m does not meet the required condition

Wrong \$m = -1/(12)\$

12

Choice-C

After analyzing the coefficients, we verified that the value of m is appropriate, maintaining the validity of the equality

Correct m = -12

13

Choice-D

Upon examining the coefficients, we found that the value of m does not meet the required condition

Wrong m = 12

14

Answer

Option

C

15

Sumup

Please summarize choices