Chapter 5, Problem 1CC

To determine

(a)

To find:

A system of equations in the variables $x,y\text{ and }z$.

Answer to Problem 1CC

A system of equations in variables $x,y\text{ and }z$ can be written as,

$\begin{array}{c}Ax+By+Cz=k\\ Ex+Fy+Gz=l\\ Px+Qy+Rz=m\end{array}$

Explanation of Solution

Calculation:

A system of equations contains the same variables in a set of equation. In the system of linear equation, each equation is linear.

A system of linear equation with a variable $x,y\text{ and }z$ can be expressed as,

$\begin{array}{c}Ax+By+Cz=k\\ Ex+Fy+Gz=l\\ Px+Qy+Rz=m\end{array}$

Here, $A,E,P$ is the coefficient of the variable $x$, $B,F,Q$ is the coefficient of variable $y$ and $C,G,R$ is the coefficient of variable $z$. The constants are $k,l,m$.

Conclusion:

A system of equations in variables $x,y\text{ and }z$ can be written as,

$\begin{array}{c}Ax+By+Cz=k\\ Ex+Fy+Gz=l\\ Px+Qy+Rz=m\end{array}$

To determine

(b)

To find:

Three methods to solve a system of equations.

Answer to Problem 1CC

Three methods to solve a system of linear equations are substitution method, elimination method and graphical method.

Explanation of Solution

Calculation:

To solve a system of linear equation three methods are used as,

Substitution method:

To solve a system of linear equation with two variable, first obtain the value of one variable in terms of second variable and then substitute it into any of the two linear equations and obtain the equation in one variable and obtain the solution.

Back substitute the solution of variable that obtained into any of the two linear equations and obtain the solution of second variable.

Elimination method:

To solve a system of linear equation with two variables by elimination method, first multiply the equation with appropriate constants to make equal coefficient for same variable.

Add or subtract the equation and obtain the equation in one variable and get the solution of that variable.

Back substitute the solution of variable that obtained into any of the two linear equations and obtain the solution of second variable.

Graphical method:

To obtain the solution of two equations with two variables by graphical method, first sketch the graph of two equations in a common screen and obtain the intersection point of the equations.

The x -coordinate and y -coordinate of intersection point of the two equations gives the solution of the linear equations.

Conclusion:

Thus, three methods to solve a system of linear equations are substitution method, elimination method and graphical method.