Final answer:
The solution to the system of equations is found by isolating x in the first equation, substituting it into the second equation, and solving for y. Then y is substituted back into the first equation to find x, resulting in x = 3.4706 and y = 4.1176.
Step-by-step explanation:
To solve the given system of equations by substitution, let's start by isolating x in the first equation.
1. Given the first equation x - 4y = -13, we can solve for x:
x = 4y - 13
2. We now substitute x into the second equation:
3x + 5y = 31 becomes:
3(4y - 13) + 5y = 31
3. Expanding and simplifying the equation we get:
12y - 39 + 5y = 31
17y - 39 = 31
4. Adding 39 to both sides gives us:
17y = 70
5. Dividing both sides by 17 we find the value of y:
y = 70 / 17
y = 4.1176
6. Substitute y back into the equation x = 4y - 13 to find x:
x = 4(4.1176) - 13
x = 16.4706 - 13
x = 3.4706
So the solution to the system of equations is x = 3.4706 and y = 4.1176.