The sum of two number is 6. twice the first number added to three times the second number is 10. write a system of equations and solve for both numbers.

4 and 2 are the required numbers which satisfies the given equations

Step-by-step explanation:

Let the two numbers be x and y

According to the first condition

their is is 6

which is

x + y =6                (i)

Now according to second condition

twice the first number i.e. 2x added to three time the second number i.e. 3y is 10

in form of equation it could be written as

2x + 3y = 10           (ii)

Now from first equation we have

x + y =6

subtracting y from both sides

x = 6 - y                    (iii)

Now putting this value of x in equation (ii)

equation (ii) is

2x + 3y = 10

Putting the value gives

2(6-y)+3y = 10

opening the brackets

12 - 2y + 3y = 10

12 - y = 10

subtracting 12 from both sides

12 - y -12 = 10 -12

it becomes

- y = -2

multiplying both sides by (-1)

it becomes

(-1)(-y) = (-2) * (-1)

y = 2

Now we got the value of y put it in equation iii which is

x = 6 -y

putting the value

x = 6 - 2

x = 4

So the two numbers are x = 4 and y = 2

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step-by-step explanation:

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