Elementary operations

Use elementary operations to solve the system of equations

Use elementary operations to find the point $(x,y)$ that lies on both lines $x+3y=1$ and $4x-y=3$.

Use elementary operations to determine whether the three lines $x+2y=1$, $2x-y=1$, and $4x+3y=3$ have a common point of intersection. If so, find the point, and if not, tell why they don’t have such a common point of intersection.

Do the three planes, $x+y-3z=2$, $2x+y+z=1$, and $3x+2y-2z=0$ have a common point of intersection? If so, find one and if not, tell why there is no such point.

Solve the following system of equations by back substitution.

Write the following system of linear equations as an augmented matrix. Caution: you first have to simplify and rearrange the equations so that “like” variables are lined up in columns. Write the variables in the order $x$, $y$, $z$.

Four times the weight of Gaston is 150kg more than the weight of Ichabod. Four times the weight of Ichabod is 660kg less than seventeen times the weight of Gaston. Four times the weight of Gaston plus the weight of Siegfried equals 290kg. Brunhilde would balance all three of the others. Find the weights of the four people.