Solve the following system of equations using substitution. What is the value of y?
2x+3y=105
x+2y=65
a. 15
b. 25
c. 40***
d. 65
x = 65 - 2 y
2 (65 - 2 y) + 3 y = 105
solve that for y
25 right?
To solve the system of equations using substitution, we'll start by solving the second equation for x in terms of y.
Given equation: x + 2y = 65
Rearrange the equation to solve for x:
x = 65 - 2y
Now substitute this expression for x in the first equation:
2x + 3y = 105
Replace x with 65 - 2y:
2(65 - 2y) + 3y = 105
Now, simplify and solve for y:
130 - 4y + 3y = 105
130 - y = 105
-y = 105 - 130
-y = -25
Dividing by -1 on both sides gives:
y = 25
Therefore, the value of y is 25.
So, the correct answer is b. 25.