The difference between six times the first number and 6 times the second number is negative twelve. The first number is nine times the second number minus ten. What are the two numbers?

Answer 1

You're going to set up a system of equations.

6x-6y=-12

x=9y-10

Now you can substitute the bottom equation into the top equation:

6 x -6y=-12

6(9y-10)-6y=-12 *Distribute and Combine Like terms

54y-60-6y=-12

48y-60=-12 *Add 60 to both sides

48y=48

y=1

x=9(1)-10

x=-1

Now you can check your answer

6(-1)-6(1)=-12

Hope this helps!

Answer 2

Miracle,

You asked -

The difference between six times the first number and 6 times the second number is negative twelve. The first number is nine times the second number minus ten. What are the two numbers?

Answer: You have to read carefully to parse the algebraic expressions from the word problem. First I'm going to define the variables:

x - first number

y - is the second number

Reading the first sentence "6 times the first number" is 6x, and 6 times the second number is 6y, the difference between them is 6x-6y is equal to -12. Here is the equation:

6x-6y=-12

Now reading the second sentence. The first number x is 9 times the second number 9y minus 10 or 9y-10. Here is the equation

x = 9y-10

Now we have two linear equations with two unknowns we can solve by graphing, substitution or addition methods. I'm going to use substitution, from the second equation

x=9y-10 I'm going to plug it into the first equation 6x-6y=-12

6(9y-10)-6y=-12; now use the distributive property and collect like terms

54y-60-6y=-12; collect like terms; add 60 to both sides to isolate the term with the variable

48y=48; divide each side by 48

y = 1; now that we know y put into the second equation and solve for x

x = 9(1)-10 = 9-10 = -1

Can you check to see if my answers are correct?

Regards,

Ray

Answer 3

First number is -1 and the second number is 1

Answer 4

Let's assign variables for the unknown numbers, say x for the first and y for the second. Now replace every occurence of "first number" with "x" and "second number" with "y" in the word problem

So

"The difference between six times the first number and 6 times the second number is negative twelve. The first number is nine times the second number minus ten. What are the two numbers?"

Becomes

"The difference between six times x and 6 times y is negative twelve. x is nine times y minus ten. What are the two numbers?"

Then translate the rest of the words into mathematical equivalents: difference means subtraction, times means multiplication, is means equals, etc.

"The difference between six times x and 6 times y is negative twelve."

becomes the equation

6x - 6y = -12

and

"x is nine times y minus ten"

becomes

x = 9y - 10

Then use substitution to solve for one of the variables, say y

6(9y - 10) - 6y = -12

54y - 60 - 6y = -12

48y = 48

y = 1

Then back substitute into the other equation to find x

x = 9(1) - 10

= -1