# Chapter 10: Systems of Equations and Inequalities

Q1.

These exercises refer to the following system:

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

If we add $2$ times the first equation to the second equation, the second equation becomes_______$=$________

Q1.

If a system of linear equations has infinitely many solutions, then the system is called____ . If a system of linear equations has no solution, then the system is called_____.

Q1.

The system of equations

$\left\{\begin{array}{l}2x+3y=7\\ 5x-y=9\end{array}\right.$

is a system of two equations in the two variables______ and_______ . To determine whether $(5,-1)$is a solution of this system, we check whether $x=5$and $y=-1$satisfy each______ in the system. Which of the following are solutions of this system?

$(5,-1),(-1,3),(2,1)$

Q10.

Elimination Method

Use the elimination method to find all solutions of the system of equations.

$\left\{\begin{array}{l}2x+5y=15\\ 4x+y=21\end{array}\right.$

Q10.

Dimension of a Matrix State the dimension of the matrix.

$\left[\begin{array}{ll}1& 0\\ 0& 1\end{array}\right]$.

Q10.

Triangular Systems

Use back-substitution to solve the triangular system

$\left\{\begin{array}{l}x-2y+3z=10\\ 2y-z=2\\ 3z=12\end{array}\right.$

Q11.

Elimination Method

Use the elimination method to find all solutions of the system of equations.

$\left\{\begin{array}{l}3x-2y=-13\\ -6x+5y=28\end{array}\right.$

Q11.

Triangular Systems

Use back-substitution to solve the triangular system

$\left\{\begin{array}{l}2x-y+6z=5\\ y+4z=0\\ -2z=1\end{array}\right.$

Q11.

The Augmented Matrix Write the augmented matrix for the system of linear equations.

$\left\{\begin{array}{l}3x+y-z=2\\ 2x-y=1\\ x-z=3\end{array}\right\}$.

Q12.

Triangular Systems

Use back-substitution to solve the triangular system

$\left\{\begin{array}{l}4x+3z=10\\ 2y-z=-6\\ \frac{1}{2}z=4\end{array}\right.$