To solve for y in the system of equations, we have the following two equations:
- Equation 1: x + 3y = 6
- Equation 2: 2x + y = 10
We can use the substitution or elimination method. For this explanation, we’ll use the substitution method.
First, let’s solve Equation 1 for x:
x = 6 - 3y
Now, we can substitute this expression for x into Equation 2:
2(6 - 3y) + y = 10
Expanding the equation gives us:
12 - 6y + y = 10
Now, combine the like terms:
12 - 5y = 10
Next, isolate y by subtracting 12 from both sides:
-5y = 10 - 12
-5y = -2
Now, divide both sides by -5:
y = \frac{-2}{-5} = \frac{2}{5}
Thus, the value of y is:
y = 0.4
In conclusion, by substituting x from one equation to another and solving, we find that y equals 0.4.