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
I think it is B??
Can you explain and show me how to work this problem?
x = 65 - 2y
2x + 3y = 105
Substitute 65-2y for x in second equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.
It definitely is not D! You are right with B.
To solve the system of equations using substitution, we need to solve one equation for one variable and then substitute that expression into the other equation. Let's solve the second equation for x.
Given:
2x + 3y = 105 ---> Equation 1
x + 2y = 65 ---> Equation 2
Let's solve Equation 2 for x:
x = 65 - 2y
Now, substitute this expression for x in Equation 1:
2(65 - 2y) + 3y = 105
Simplify the equation:
130 - 4y + 3y = 105
130 - y = 105
Subtract 130 from both sides of the equation:
-y = 105 - 130
-y = -25
Multiply both sides of the equation by -1 to solve for y:
y = 25
Therefore, the value of y is 25.
So, the correct answer is B.