A number is 9 more than another number. Twice the sum of the two numbers is 10. Find the two numbers.

7, -2

Step-by-step explanation:

we call the first number "X" and the second one "Y"

X is 9 more than Y! which means we need to add 9 to Y so it'll be equal to X. so: Y+9=X

also 2×(X+Y)=10

you can also write this down as: 2X+2Y=10

now we have:

X=Y+9

2X+2Y=10

you can now put what equals to X in the second Equation:

2(Y+9)+2Y=10 => 2Y+18+2Y=10 => 4Y=10-18 =>Y= -2

the only thing left to do is to put Y= -2 in the first equation:

X= -2+9 => X=7

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.