1

Problem

If there is no solution of the linear equation system Sg - 7h = 9, 3g + 5h =11, then find the value of S?

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

Step

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 Sg - 7h = 9 with equation (1) and 3f + 5h = 11 with equation (2). So by comparing the coefficients, we can write.

\$a_1 = S, a_2 = 3, b_1 = - 7, b_2 = 5, c_1 = 9, c_2 = 11\$

5

Step

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

\$ S/3 = - 7/5 ne 9/(11) \$ …​…​.equation (3)

\$ S/3 = - 7/5 \$

\$ 5S = - 21\$

6

Step

Divide by 5 into both sides then after simplification:

\$ (\cancel(5^1)k)/(\cancel5^1)\$

\$ S = - (21)/5 \$

7

Solution

Therefore, the value of S is \$ -( 21)/5 \$.

8

Sumup

Please summarize steps

Choices

9

Choice-A

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

Correct \$S = - (21)/5\$

10

Choice-B

This is the reciprocal of the correct answer, which is incorrect

Wrong \$S = 5/(21)\$

11

Choice-C

This is the negation of the correct answer, which is incorrect

Wrong \$S = (21)/5\$

12

Choice-D

This is the reciprocal of the negation of the correct answer, which is incorrect

Wrong \$S = - 5/(21)\$

13

Answer

Option

A

14

Sumup

Please summarize choices