1

Problem

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

-x + 6y = 9 and hy - px = 81

2

Step

The given system of equation are

-x + 6y = 9 equation(1) and

hy - px = 81 equation(2)

3

Step

Equation(1) is multiply by the number is 9:

9(-x + 6 y = 9)

-9x + 54 y = 81 euqation(3)

4

Hint

Since both equations (2) and (3) are now equal to 81. So , now set them equal to each other.

5

Step

Then find values of h and p:

hy - px = -9x + 54y

hy - px = 54y - 9x

So, here h = 54 and p = 9

6

Step

Then now find the value if h - p:

h - p = 54 - 9

h - p = 45

7

Solution

So therefore the value of h - p = 45.

8

Sumup

Please summarize steps

Choices

9

Choice-A

This is wrong due to miscalculations

Wrong 50

10

Choice-B

This is correct due to accurately done the calculations

Correct 45

11

Choice-C

This is wrong due to miscalculations

Wrong 40

12

Choice-D

This is wrong due to miscalculations

Wrong 54

13

Answer

Option

B

14

Sumup

Please summarize choices