Solve the system of equations by the substitution method. If the system does not have a single ordered pair as a solution, state whether the system is incons istent or dependent
$x=y+3\\x=-3$

Consider

$$A=\left[\begin{array}{rrrr} 2 & 4 & 6 & 18 \\ 4 & 5 & 6 & 24 \\ 3 & 1 & -2 & 4 \end{array}\right]$$

. Determine an LU factorization of $A$ using the elementary row operations to move $A$ to a row echelon matrix keeping track of the elementary matrices that correspond to the row operations you use. Express $L$ as the product of elementary matrices.

The first of these equations plus the second equals the third: x + y + z = 2; x + 2y + z = 3; 2x + 3y + 2z = 5. The first two planes meet along a line. The third plane contains that line, because if x, y, z satisfy the first two equations then they also _____. The equations have infinitely many solutions (the whole line L). Find three solutions.

Draw the two pictures in two planes for the equations x - 2y = 0, x + y = 6.

Describe the intersection of the three planes u + v + w + z = 6 and u + w + z = 4 and u + w = 2 (all in four-dimensional space). Is it a line or a point or an empty set? What is the intersection if the fourth plane u = -1 is included? Find a fourth equation that leaves us with no solution.

*For

$$A=\left[\begin{array}{rr}2 & -5 \\ 1 & 3\end{array}\right]$$

and

$$B=\left[\begin{array}{rr}-1 & -3 \\ 5 & 2\end{array}\right]$$

, determine the following.*
$A-2 B$

Graph the syst em of linear inequalities and indicat e the solution set. \

$$y \leq 3x \\ x \leq 3y$$

Solve the system of equations by the addition method . If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. \

$$2x+y=2 \\ -3-y=5$$

*For

$$A=\left[\begin{array}{rr}2 & -5 \\ 1 & 3\end{array}\right]$$

and

$$B=\left[\begin{array}{rr}-1 & -3 \\ 5 & 2\end{array}\right]$$

, determine the following.* \

$$A+B$$

Solve the system of equations by the substitution method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent \

$$3 x+y=1 \\ 3 y=-9 x-4$$

Determine which ordered pairs are solutions to the given system. x+2y=6, (-2, 4), (2, 2), (3, -9), x-y=-6

Graph the syst em of linear inequalities and indicat e the solution set. \

$$x - 3y \leq 3 \\ x+2y \geq6$$

Determine which ordered pairs are solutions to the given system. y=4x-2, (2, 6), (3, -10), (1, 7), y=-x+8

Solve the system of equations by the substitution method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent \

$$2 x-y=4 \\ 3 x-y=2$$