Final answer:
To solve the system of equations using the substitution method, you need to find an expression that can be substituted for x in equation 1. By rearranging the second equation and substituting the expression for x in equation 1, you can solve for y. By then substituting the value of y back into equation 1, you can solve for x.
Step-by-step explanation:
To solve the system of equations by substitution method, we need to find an expression that we can substitute for x in equation 1. Let's rearrange the second equation, x + 2y = 3, to solve for x:
x = 3 - 2y
Now we can substitute this expression for x in equation 1:
6(3 - 2y) - 5y = 13
Simplify:
18 - 12y - 5y = 13
Combine like terms:
-17y = -5
Divide both sides by -17:
y = 5/17
Now, substitute this value of y back into equation 1 to solve for x:
6x - 5(5/17) = 13
Simplify:
6x - (25/17) = 13
Add (25/17) to both sides:
6x = 13 + (25/17)
Simplify:
6x = (221 + 25)/17
Combine like terms:
6x = 246/17
Divide both sides by 6:
x = (246/17)/6
Simplify:
x = 246/102
Therefore, the expression that can be substituted for x in equation 1 to solve the system by substitution is x = 246/102.