Final answer:
To solve the given system of equations using substitution, solve one equation for one variable and substitute it into the other equation. The solution is x = 1 and y = 5.
Step-by-step explanation:
To solve the given system of equations using substitution, we need to solve one equation for one variable and substitute it into the other equation. Let's solve the first equation for x:
3x + 2y = 13
3x = 13 - 2y
x = (13 - 2y)/3
Now substitute this value of x into the second equation:
5((13 - 2y)/3) + 2y = 15
Simplify,
(65 - 10y)/3 + 2y = 15
Multiply both sides by 3 to eliminate the fraction:
65 - 10y + 6y = 45
Combine like terms:
-4y = -20
Divide both sides by -4:
y = 5
Now substitute this value of y back into the first equation to find x:
3x + 2(5) = 13
3x + 10 = 13
3x = 3
x = 1
Therefore, the solution to the system of equations is x = 1 and y = 5.