word problem?

Question

2 times the first number decreased by 6 is 3 times the second number. The sum of twice the first number and 3 times the second number is 6. Find the numbers.

Answer 1

by the given conditions eqn.s r
2x-3y=6
2x+3y=6
x=3
y=0
first no.=3
second no.=0

Answer 2

Let x be the first number
Let y be the second number

2 times the first number decreased by 6 is 3 times the second number
2x - 6 = 3y

The sum of twice the first number and 3 times the second number is 6
2x + 3y = 6

rearrange equation one gives:
2x - 3y = 6

add equation 1 + equation 2:

2x + 3y = 6
2x - 3y = 6
4x = 12
x = 3

resub x=3 into one of the original equations:
2(3) - 3y = 6
-3y = 0
y = 0

Answer 3

You will need to look for key words in the sentence that tell you what operation to use. Sometimes they might be simple, like "add" means + or "product" means multiply. In your question, "times" will be the easy keywords, but "decreased by" is a tricky one.

Since we have 2 different numbers, choose 2 variables.

Let x = 1st number
Let y = 2nd number

According to the first sentence:
2 times (multiplied by) x (1st number) decreased by (subtract) 6 is (equals) 3 times y (2nd number) so "2x - 6 = 3y"

The second sentence translates to:
The sum of (add the next two things together) x and 3y is 6. So "x + 3y = 6".

Use those 2 equations and solve them using one of a few options.

2x - 6 = 3y and 2x + 3y = 6

One method that can be used is cancelling. To do this, you add or subtract the 2 equations to make one of the variables cancel out. Notice how we have 2x in each equation. If we subtract the 2 equations, these add to 0 and will cancel each other out.

2x - 6 = 3y
-(2x + 3y = 6)

-3y - 6 = 3y - 6 Solve by adding +6 to both sides.
-3y = 3y Add +3y to both sides to cancel the -3y on the left
0 = 6y Divide by 6.
y = 0

Now that you have one of the numbers (the second one), you can find the first by plugging it back into one of the original equations.

2x - 6 = 3y
2x - 6 = 3(0)
2x - 6 = 0 Add 6 to both sides to cancel the -6 on the left.
2x = 6 Divide by 2
x = 3.

So your answers are:
first number is 3
second number is 0

Answer 4

Let the numbers be x and y
2x - 6 = 3y which leads to 2x - 3y = 6
Also 2x + 3y = 6

Adding the equations:-
4x = 12
x = 3
But 2x + 3y = 0 therefore 6 + 3y = 6
3y = 0
y = 0

The numbers are 3 and 0

Answer 5

2x-6=3y
2x+3y=6

Solve the first equation for x or y. I'm solving for x.
x=[3y+6]/2
Substitute x back into the 2nd equation.
2([3y+6]/2)+3y=6
y = 0
Substitute y into 1st or 2nd equation to get x.
2x+3(0)=6
x = 3

Answer 6

2x-6=3y
2x-3y=6.......(1)
2x+3y=6.......(2)
so 4x=12
and x=3
putting the value of x in the eq. 1
Y=0
nos are 3 & 0