We have two numbers, let's say a and b.
We must build our equations.
Sum = addition, and twice = multiplication, so:
[tex]2a + b = 61[/tex]
where a represents "twice a number"
Less = subtraction, and four times = multiplication, so:
[tex]b = 4a - 17[/tex]
Now we have our two equations:
[tex]2a + b = 61\\b = 4a - 17[/tex]
One of these is already solved for a variable, so we can substitute it.
Substitute b into the first equation:
[tex]2a + 4a - 17 = 61\\6a - 17 = 61\\6a = 78\\a = 13[/tex]
We have solved for a's int value, being 13.
Plug a into the second equation and solve for b:
[tex]b = 4(13) - 17\\b = 52 - 17\\b = 35[/tex]
We have solved for b's integer value, 35.
Now that we have both numbers, let us check our solution:
a = 13
b = 35
The sum of twice a number and a second number is 61:
13(2) + 35 = 26 + 35 = 61 ✓
The second number is 17 less than four times the first:
35 = 4(13) - 17 = 52 - 17 = 35 ✓
Our answers are:
a = 13
b = 35
