Solve for y x+y=9 x=5

Solution:

Step:1

Substitute $5$ for $x$ in each equation.

Step:1.1

In the equation $x + y = 9$, replace $x$ with $5$ to get $(5) + y = 9$. Also, remember that $x = 5$.

Step:1.2

Combine like terms on the left side.

Step:1.2.1

Eliminate the parentheses to have $5 + y = 9$. Keep in mind that $x = 5$.

Step:2

Solve for $y$ to get $y = 4$, and recall that $x = 5$.

Knowledge Notes:

To solve a system of equations where one variable is already given, you can follow these steps:

1. Substitution: When one variable is known, you can substitute its value into any equation that contains that variable. This simplifies the equation, making it easier to solve for the remaining unknowns.

2. Simplifying the Equation: After substitution, simplify the equation by performing any necessary arithmetic operations, such as adding or subtracting terms, to isolate the unknown variable.

3. Solving for the Variable: Once the equation is simplified, solve for the remaining variable by isolating it on one side of the equation.

In the given problem, we have a system of two equations with two variables, $x$ and $y$. The value of $x$ is given as $5$. By substituting $5$ for $x$ in the first equation, we simplify the equation to find the value of $y$. The process involves basic algebraic steps and the use of substitution to solve for the second variable.

The use of LaTeX in the solution helps to clearly present the mathematical expressions and equations. LaTeX is a typesetting system that is widely used for the communication and publication of scientific documents in many fields, including mathematics, computer science, engineering, physics, chemistry, and economics. It allows for the precise formatting of formulas and equations for printed and digital documents.