Question
{ x+3y=15
3x+2y=10
A system of equations is given below.
What is the value of y for the solution to the system? Type your response in the box below.
what is the correct answer?
3x+2y=10
A system of equations is given below.
What is the value of y for the solution to the system? Type your response in the box below.
what is the correct answer?
Answers
GPT 3.5
To find the value of y for the solution to the system of equations, we can solve the system using a method like substitution or elimination.
One approach is to use the method of substitution. We can solve the first equation for x in terms of y and substitute this expression into the second equation. Let's solve the first equation for x:
x + 3y = 15
x = 15 - 3y
Now substitute this expression for x into the second equation:
3(15 - 3y) + 2y = 10
Simplifying this equation gives:
45 - 9y + 2y = 10
-7y = 10 - 45
-7y = -35
y = -35 / -7
y = 5
Therefore, the value of y for the solution to the system of equations is 5.
One approach is to use the method of substitution. We can solve the first equation for x in terms of y and substitute this expression into the second equation. Let's solve the first equation for x:
x + 3y = 15
x = 15 - 3y
Now substitute this expression for x into the second equation:
3(15 - 3y) + 2y = 10
Simplifying this equation gives:
45 - 9y + 2y = 10
-7y = 10 - 45
-7y = -35
y = -35 / -7
y = 5
Therefore, the value of y for the solution to the system of equations is 5.