1

Problem

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

2y = - x + 25 and gx = - hy + 100

2

Step

The given system of equation are

2y = - x + 25 equation(1) and

gx = - hy + 100 equation (2)

3

Step

Equation(1) is multiply by the number is 4:

4(2y = -x + 25)

4x + 8y = 100 equation(3)

4

Hint

Since both equations (2) and (3) are now equal to 100, now set them equal to each other.

5

Step

Then find the values of g and h:

gx + hy = 4x + 8y

So, here g = 4 and h = 8

6

Step

Now then find the value of g:h :

g : h = 4 : 8

g : h = 1 : 2

7

Solution

So, the value of g : h = 1 : 2.

8

Sumup

Please summarize steps

Choices

9

Choice-A

This is not correct because it is double the correct answer

Wrong 4 : 8

10

Choice-B

Correct because it satisfies the condition for infinitely many solutions

Correct 1 : 2

11

Choice-C

Incorrect because it implies g : h = 2 : 1, which contradicts g : h = 1 : 2

Wrong 8 : 4

12

Choice-D

This is not correct due to mistake in calculation

Wrong 2 : 1

13

Answer

Option

B

14

Sumup

Please summarize choices