To find the value of y in the system of equations, we first need to solve the two equations simultaneously:
1. 3x + 5y = 1 (Equation 1)
2. 7x + 4y = 13 (Equation 2)
We can use the method of substitution or elimination. Here, we’ll use the substitution method:
From Equation 1, we can express x in terms of y:
3x = 1 – 5y
x = (1 – 5y)/3
Now, we can substitute this value of x into Equation 2:
7((1 – 5y)/3) + 4y = 13
Multiplying through by 3 to eliminate the fraction gives:
7(1 – 5y) + 12y = 39
7 – 35y + 12y = 39
-35y + 12y = 39 – 7
-23y = 32
y = -32/23
Thus, the value of y in this system of equations is:
y ≈ -1.39
This means that for the given system of equations, the solution yields y approximately equal to -1.39.