x+y = 23, so y = 23-x
7x-5y = 5, but y = 23-x from above, so
7x-5(23-x) = 5
7x-115+5x = 5
7x+5x = 5+115
12x = 120
x = 10.
x+y = 23
10+y = 23
so y = 23-10 = 13.
The sum of two numbers is 23. Seven times the first number less five times the second number is equal to 5. What are the two numbers?
Now, i have worked this out and the numbers i get equal 23 but are not the numbers given as the answer in the book. Take a look:
x + y = 23
7x - 5y = 5
7(23 - y) - 5y = 5
161 - 7y - 5y = 5
161 - 2y = 5
2y = 156
y = 78
Put the numbers into the equation: -55 + 78 = 23
So the answer i get appears to be correct because it works. But like i said, the answer in the back of the book is 10 + 13 = 23
So where did i go wrong? And if algebra lead me to my answer (-55 + 78 = 23) which makes the equation true, why can't my answer be the right answer?