X+3y=15
3x+2y=10
What is the value of y for the solution to the system
To find the value of y for the solution to the system of equations, we can solve the system by elimination or substitution.
1. Elimination:
First, we can multiply the first equation by 2 and the second equation by -3 to make the coefficient of x the same and eliminate it when we subtract the equations:
2(x + 3y) = 2(15)
-3(3x + 2y) = -3(10)
Simplifying:
2x + 6y = 30
-9x - 6y = -30
Now, we can add the two equations together to eliminate y:
(2x + 6y) + (-9x - 6y) = 30 + (-30)
-7x = 0
Dividing by -7 gives:
x = 0
Now, we can substitute x = 0 into one of the original equations to solve for y:
0 + 3y = 15
3y = 15
y = 15/3
y = 5
Therefore, the value of y for the solution to the system of equations is y = 5.
2. Substitution:
We can solve one of the equations for x and substitute it into the other equation:
From the first equation, we have:
x = 15 - 3y
Substituting this into the second equation:
3(15 - 3y) + 2y = 10
Simplifying:
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 y = 5.