I have problem solving this system

Question

I have given arithmetic progression and I know that:

the sum of the first element(A1) and the fifth element(A5) is equal to 18

A1+ A5 = 18

and that the sum of the first and the third element minus the seventh element is equal to 1

A1 + A3 - A7 = 1

and I have this system

A1 + A5 = 18
A1 + A3 - A7 = 1

and when I use the properties of arithmetic progression the system looks this way:

A1 + A1 + 4d = 18
A1 + A1 + 2d - A1 + 6d = 1

2*A1 + 4d = 18
2*A1 + 2d - A1 + 6d = 1
//I can devide the first equation by two 
A1 + 2d = 9
2*A1 + 2d - A1 + 6d = 1

and from here I aways make mistake somewhere could anybody give me a little hit? I have to find the sum of the first 10 elements of the progression. The answer of the question is 140(the sum of the first 10 elements is 140 but this isn't given in the description)

Answer 1

$$A1+A3-A7=A1+(A1+2d)-(A1+6d)=A1-4d$$ and not $$A1+8d$$

Then you should be able to solve for $A1,d$

Now the sum of $n(>0)$ elements $$\frac n2[2\cdot A1+(n-1)d]$$