The sum of two numbers is 10. one number is two less than three times the other. find the numbers.

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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step-by-step explanation: