Solve for y x+y=7
Given a problem: Solve for y x+y=7
Brief explanation of the question:
The question is asking to find the value of the variable y in the equation x + y = 7. This is a linear equation with two variables, x and y. To solve for y, the value of x needs to be either given or isolated, and y must be expressed in terms of x. The solution will show the relationship between x and y that satisfies the equation.
$x + y = 7$
Answer
Solution:
Step 1:
To isolate $y$, we remove $x$ from the left side by subtracting it from both sides of the equation, resulting in $y = 7 - x$.
Knowledge Notes:
The given problem is a simple linear equation in two variables, $x$ and $y$. The goal is to solve for $y$ in terms of $x$. The problem-solving process involves algebraic manipulation to isolate the variable of interest on one side of the equation.
Here are the relevant knowledge points for this problem:
Linear Equations: A linear equation is an equation between two variables that gives a straight line when plotted on a graph. The general form of a linear equation in two variables, $x$ and $y$, is $ax + by = c$, where $a$, $b$, and $c$ are constants.
Isolating a Variable: To solve for one variable in terms of the others, we isolate the desired variable on one side of the equation. This often involves using inverse operations like addition/subtraction or multiplication/division.
Inverse Operations: These are operations that undo each other. For example, addition and subtraction are inverse operations, as are multiplication and division. To solve an equation, we often use inverse operations to move terms from one side of the equation to the other.
Maintaining Equality: When solving equations, it is crucial to perform the same operation on both sides of the equation to maintain equality. If you subtract a term from one side, you must subtract the same term from the other side.
In this case, since we have $x + y = 7$ and we want to solve for $y$, we subtract $x$ from both sides of the equation to isolate $y$. This gives us $y = 7 - x$, which is the solution to the equation in terms of $y$.
