Solve the following system of equations using substitution. What is the value of y?
2x+3y=105
x+2y=65
To solve the system of equations using substitution, we will solve one equation for one variable and substitute it into the other equation.
We can solve the second equation for x:
x + 2y = 65
x = 65 - 2y
Now we substitute this expression for x in the first equation:
2(65 - 2y) + 3y = 105
Distribute the 2:
130 - 4y + 3y = 105
Combine like terms:
-y + 130 = 105
Subtract 130 from both sides:
-y = -25
Multiply both sides by -1 to solve for y:
y = 25
The value of y is 25.