Q. 200 - Intermediate Algebra

Question

Write the system of equations that corresponds to the augmented matrix: $\left[\begin{array}{rrr}2& -1& 4\\ 1& -3& 2\end{array}\right]$

Step-by-Step Solution

Answer

The required system of linear equations is $\left\{\begin{array}{l}2x-y=4\\ x-3y=2\end{array}\right.$.

Step 1. Given information.

Consider the given augmented matrix,

$\left[\begin{array}{rrr}2& -1& 4\\ 1& -3& 2\end{array}\right]$

We know in an augmented matrix, each row corresponds to an equation. The vertical line replaces the equal sign in the equation. As this matrix is a $2\times 3$.

Step 2. Write the matrix into the system of equations.

Write into the system of equation with two variables,

$\left\{\begin{array}{l}2x-y=4\\ x-3y=2\end{array}\right.$