1

Problem

Find the value of l and m:

32l = - 8m + 11 and 48l + 12m = 17.

2

Step

Given equations are

\$32l = - 8m + 11\$

\$48l + 12m = 17\$

3

Step

Now rewrite the first equation:

\$32l + 8m = 11\$ …​…​.equation (1)

\$48l + 12m = 17\$ …​…​.equation (2)

4

Step

Solve for l value:

\$l = - \cancel8^1/\cancel32^4 m + (11)/(32)\$

\$l = - 1/4 m + (11)/(32)\$

5

Step

Substitute l value in equation (2) then simplified:

\$ 48(- 1/4 m + (11)/(32)) + 12m = 17\$

\$- \cancel(48)^(12)/\cancel4^1 y + 11/\cancel(32)^2 \times \cancel(48)^3 + 12m = 17\$

\$ - 12m + 33/2 + 12m = 17\$

6

Step

Move constant terms to the right side then simplification:

\$ - 12y + 12y = 17 - (33)/2 \$

\$ 0 = (34 - 33)/2 \$

\$ 0 = 1/2 \$

7

Hint

We get \$0 = 1/2\$. This cannot be true.

8

Solution

Hence, the system of equations has no solution.

9

Sumup

Please summarize steps

Choices

10

Choice-A

This is wrong.There cannot be infinitely many solutions since there are no solutions at all

Wrong Finite solutions

11

Choice-B

Correctly reflects the outcome of the solution process, indicating that the system of equations does not have a solution

Correct No solutions

12

Choice-C

This option is wrong. It means to implies that the system has a specific, finite number of solutions

Wrong Infinite solutions

13

Choice-D

This option is wrong because it does not accurately reflect the outcome of the solution process

Wrong None of these

14

Answer

Option

B

15

Sumup

Please summarize choices