Solve for x, and x2. 4 5 X1 19 3 2 X2 9 (Simplify your answers. Type integers or fractions.)
Solve for x, and x2. 4 5 X1 19 3 2 X2 9 (Simplify your answers. Type integers or fractions.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
![**Solving Systems of Linear Equations Using Matrices**
In this exercise, we are given a system of linear equations represented in matrix form. Your task is to solve for the variables \(x_1\) and \(x_2\).
The matrix equation given is:
\[
\begin{pmatrix}
4 & 5 \\
3 & 2
\end{pmatrix}
\begin{pmatrix}
x_1 \\
x_2
\end{pmatrix}
=
\begin{pmatrix}
19 \\
9
\end{pmatrix}
\]
### Explanation:
1. The left matrix \(
\begin{pmatrix}
4 & 5 \\
3 & 2
\end{pmatrix}
\) represents the coefficients of the variables \(x_1\) and \(x_2\).
2. The middle matrix \(
\begin{pmatrix}
x_1 \\
x_2
\end{pmatrix}
\) represents the unknown variables we need to solve for.
3. The right matrix \(
\begin{pmatrix}
19 \\
9
\end{pmatrix}
\) represents the constants from the right-hand side of each equation.
To solve the equation, follow these steps:
- You can use matrix inversion, Gaussian elimination, or other methods for solving linear systems.
### Steps to Solve:
1. Write down the system of equations from the matrix representation:
\[
4x_1 + 5x_2 = 19
\]
\[
3x_1 + 2x_2 = 9
\]
2. Use an appropriate method to solve for the variables \(x_1\) and \(x_2\).
3. Simplify your answers and write them in integer or fraction form as required.
The answer format is:
\[
x_1 = \boxed{}
\]
\[
x_2 = \boxed{}
\]
(Simplify your answers. Type integers or fractions.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff60bf7ae-3e0a-47f1-9493-b686204b7388%2F812879f7-a2c0-4b25-bb97-33ba9bcc8ac9%2Fp6df62b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solving Systems of Linear Equations Using Matrices**
In this exercise, we are given a system of linear equations represented in matrix form. Your task is to solve for the variables \(x_1\) and \(x_2\).
The matrix equation given is:
\[
\begin{pmatrix}
4 & 5 \\
3 & 2
\end{pmatrix}
\begin{pmatrix}
x_1 \\
x_2
\end{pmatrix}
=
\begin{pmatrix}
19 \\
9
\end{pmatrix}
\]
### Explanation:
1. The left matrix \(
\begin{pmatrix}
4 & 5 \\
3 & 2
\end{pmatrix}
\) represents the coefficients of the variables \(x_1\) and \(x_2\).
2. The middle matrix \(
\begin{pmatrix}
x_1 \\
x_2
\end{pmatrix}
\) represents the unknown variables we need to solve for.
3. The right matrix \(
\begin{pmatrix}
19 \\
9
\end{pmatrix}
\) represents the constants from the right-hand side of each equation.
To solve the equation, follow these steps:
- You can use matrix inversion, Gaussian elimination, or other methods for solving linear systems.
### Steps to Solve:
1. Write down the system of equations from the matrix representation:
\[
4x_1 + 5x_2 = 19
\]
\[
3x_1 + 2x_2 = 9
\]
2. Use an appropriate method to solve for the variables \(x_1\) and \(x_2\).
3. Simplify your answers and write them in integer or fraction form as required.
The answer format is:
\[
x_1 = \boxed{}
\]
\[
x_2 = \boxed{}
\]
(Simplify your answers. Type integers or fractions.)
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