Solve each system by substitution.
4x + 3y = -13
-x + y = 5

Verified step by step guidance

1. Start with the given system of equations: \[4x + 3y = -13\] \[-x + y = 5\]
2. Solve the second equation for one variable, for example, solve for \(y\): \[y = x + 5\]
3. Substitute the expression for \(y\) from the second equation into the first equation: \[4x + 3(x + 5) = -13\]
4. Simplify and solve the resulting equation for \(x\): \[4x + 3x + 15 = -13\] Combine like terms and isolate \(x\).
5. Once you find the value of \(x\), substitute it back into the expression for \(y\) (i.e., \(y = x + 5\)) to find the value of \(y\).

Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations with the same variables. The goal is to find values for the variables that satisfy all equations simultaneously. In this problem, the system includes two equations with variables x and y.

Substitution Method

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation. This reduces the system to a single equation with one variable, making it easier to solve. After finding one variable, substitute back to find the other.

Solving Linear Equations

Solving linear equations means isolating the variable to find its value. This often involves operations like addition, subtraction, multiplication, or division. Accurate manipulation of equations is essential to correctly determine the values of variables in the system.