Final answer:
The solution to the system of equations is x = 0.5 and y = 4.5.
Step-by-step explanation:
To solve the system of equations x - 3y = -13 and 5x + 7y = 34, we can use the method of substitution.
First, solve the first equation for x in terms of y:
x = -13 + 3y
Substitute this expression for x into the second equation:
5(-13 + 3y) + 7y = 34
-65 + 15y + 7y = 34
22y = 99
y = 99/22
Simplify the fraction:
y = 4.5
Substitute this value of y back into the first equation to find x:
x - 3(4.5) = -13
x - 13.5 = -13
x = -13 + 13.5
x = 0.5
Therefore, the solution to the system of equations is x = 0.5 and y = 4.5.