Question

The sum of two numbers is 10. One number is two less than three times the other. Find the numbers.

Answer 1

Answer:

x = 7; y = 3

Step-by-step explanation:

Set your system of equation. Let one number = x, and the other = y.

x + y = 10

3y - 2 = x

Plug in 3y - 2 for x in the first equation.

(3y - 2) + y = 10

Simplify. Combine like terms.

3y + y - 2 = 10

4y - 2 = 10

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, add 2 to both sides.

4y - 2 (+2) = 10 (+2)

4y = 10 + 2

4y = 12

Next, divide 4 from both sides.

(4y)/4 = (12)/4

y = 12/4

y = 3

Plug in 3 for y in one of the equations.

x + y = 10

x + 3 = 10

x + 3 (-3) = 10 (-3)

x = 10 - 3

x = 7

x = 7; y = 3

Check:

x + y = 10

(7) + (3) = 10

(10) = 10 (True).

3y - 2 = x

3(3) - 2 = (7)

9 - 2 = 7

7 = 7 (True).

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Answer 2

To find the numbers, we can set two equation.

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

As the sum of them is 10:

x+y = 10

y=10-x...(1)

One number is two less than three times the other:

3x-2 = y...(2)

Put (1) into (2),

3x - 2 = 10 - x

Put the unknown to one side:

3x +x = 10+2

4x = 12

x = 12÷4

x = 3

Put x= 3 into (1),

y = 10 - (3)

y = 7

Therefore, the numbers are 7 and 3 respectively.

Hope it helps!