Solve this formula for $y$:
$\begin{array}{l}
5 x+4 y=-1 \\
y=\frac{-6}{4}
\end{array}$
Answer (1)
The problem provides a system of equations and asks to solve for y .
The value of y is directly given as y = 4 − 6 .
Simplify the fraction to get y = 2 − 3 .
The final answer is − 2 3 .
Explanation
Analyze the problem We are given the system of equations:
5 x + 4 y = − 1 y = 4 − 6
We are asked to solve for y .
Solve for y The second equation directly gives us the value of y :
y = 4 − 6
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
y = 4 ÷ 2 − 6 ÷ 2 = 2 − 3
As a decimal, this is:
y = − 1.5
Final Answer Therefore, the solution for y is:
y = 2 − 3 = − 1.5
Examples
In real-world scenarios, solving for a variable like 'y' in a system of equations is akin to determining a specific ingredient amount in a recipe or calculating a precise component value in an engineering design. For instance, if you're mixing a cleaning solution where 'x' represents the amount of water and 'y' represents the amount of concentrate, and you know the total volume and the ratio needed, solving for 'y' tells you exactly how much concentrate to add. This ensures the solution is effective without being wasteful or harmful. Similarly, in financial planning, 'y' could represent the amount to invest in a particular asset to achieve a desired overall portfolio balance, given other investment constraints represented by 'x'.
