Linear Algebra: Solving Systems of Linear Equations

Consider the following two equations: $2x + 3y = 8$ and $5x - 3y = -1$. How can we solve these two equations using elimination?

Solve the system of equations using elimination: $2x + 5y = 19$ and $x - 2y = -4$.

Given the equations $y = 5 - 2x$ and $4x + 3y = 13$, solve for $x$ and $y$ using substitution.

Use substitution to solve the system of equations: $y = 3x + 2$ and $y = 7x - 6$.

Solve for $x$ and $y$ using substitution in the following system: $4x + 2y = 14$ and $3x - 5y = -22$.

Solve the system of equations: $7x + 5y = -12$ and $3x - 4y = 1$ using any method such as graphing, elimination, and substitution.

Given two linear equations in standard form, solve the system of equations by graphing to find the intersection point.

Given two linear equations in slope-intercept form, solve the system of equations by graphing to find the intersection point.

Graph the two parallel lines representing the linear equations and determine if the system has no solution.

Graph coincident lines of the linear equations to show that the system has infinitely many solutions.

Using Gauss-Jordan elimination, solve the system of linear equations given by the augmented matrix: $\begin{bmatrix} 1 & -1 & 3 & | & 8 \\ 1 & 1 & 2 & | & 1 \\ 3 & 1 & 4 & | & 10 \end{bmatrix}$

Solve the system of linear equations using the Gauss-Jordan elimination method.

Solve the following system of equations using Gauss-Jordan elimination: \begin{align*} 2x - 5y &= 15 \\ 3x + y &= 31 \end{align*}

Using Gaussian elimination, solve the system of linear equations represented by the matrix.

Solve the given system of two equations with two variables using the Gaussian elimination method.

Determine whether the following homogeneous system has non-trivial solutions by inspection: 3 equations with 4 unknowns (X1 through X4). Since there are more unknowns than equations, it is guaranteed that this homogeneous linear system will have infinitely many solutions.

Solve the following homogeneous linear system using Gaussian elimination. The system matrix is provided, and the constants are all zero. Determine the type of solutions (trivial or infinitely many) the system possesses.

Solve the system of equations: $5x + 4y = 0$ and $2x - 2y = 0$, using elimination by addition to find the trivial solution.

Solve the system of equations: $x_1 - 2x_2 + x_3 = 0$, $6x_2 - 3x_3 = 0$, and $x_1 - 2x_2 - x_3 = 0$, using row reduction to demonstrate that it only has the trivial solution.