System of equations

Question

the sum of twice a number and triple a different number is equivalent to seventy two. But take half of that first number and increase it by eight and it will be equal to a third of that different number. What are he two numbers?

Answer 1

Two numbers: x and y

2x+3y=72

x/2+8=y/3 (multiply both sides by 6)

 

2x+3y=72
3x-2y=-48

If you solve it, you have to get

x = 0, y =24

Answer 2

2x + 3y = 72    {equation 1}

 

x/2 + 8 = y/3

Multiply through by 6 ... LCM of 2, 3

3x + 48 = 2y  

3x - 2y = -48{equation 2}

 

we have two equations with two unknowns.  Let's use 

elimination.  Multiply equation 1 by 2 and equation 2 by 3

 

4x + 6y = 144

9x - 6y = -144   add equations

--------------------

13x = 0

x = 0

 

2x + 3y = 72

3y = 72

y = 24

 

The numbers are 0, 24

 

Answer 3

Hello Briana,

 

Using the first sentence, we have:

2x + 3y = 72

 

For the second sentence, we get:

(1/2)x + 8 = (1/3)y

 

Now, I don't like fractions as it is, and even less so when I can't true-type them, so I am going to multiply the second equation by 6 to clear the fractions.  Why 6?  Because it is the least common denominator of 2 and 3.

 

So the second equation becomes:

3x + 48 = 2y. Rearranging so that x and y are on the same side, we get:

3x - 2y = -48. 

 

Now I am going to multiply this equation by 3, and the first equation by 2, so that I have the same amount of y's to use 'elimination  method'.

 

      9x - 6y = -144

+ (4x + 6y = 144)

--> 13x = 0

--> x = 0

 

Plugging this back into the first equation, we have:

2(0) +3y = 72

--> y = 24

 

So the two numbers are 0 and 24.

 

Thank you for the question, and have a wonderful day!

Kind regards,

Michael Ehlers