1

Problem

In the system of equations above, s and m are constants. If the system has infinitely many solutions, what is the value of sm:

sx + my = 12 and 3x + 12y = 6

2

Step

The given system of equation are

sx + my = 12 equation(1) and

3x + 12y = 6 equation(2)

3

Step

Equation(2) is multiply by the number is 2:

2(3x + 12y = 6)

6x + 24 y = 12 equation(3)

4

Hint

Since both equations (1) and (3) are now equal to 12, now set them equal to each other.

5

Step

Then find the values of s and m:

sx + my = 6x + 24 y

So, here s = 6 and m = 24

6

Step

Find the value of sm:

\$sm = 6 \times 24\$

sm= 144

7

Solution

So, therefore the value of sm is 144.

8

Sumup

Please summarize steps

Choices

9

Choice-A

This is correct value obtained from the solution of the equations

Correct 144

10

Choice-B

This is not the correct value obtained from the solution of the equations

Wrong 410

11

Choice-C

This is not the correct value obtained from the solution of the equations

Wrong 414

12

Choice-D

This is not the correct value obtained from the solution of the equations

Wrong 140

13

Answer

Option

A

14

Sumup

Please summarize choices