Chapter 6, Problem 7SGR

To determine

To state: The given statement is true or false. If false replace underlined term to make a true sentence.

Answer to Problem 7SGR

The given statement is false. The true statement is:

The set of two or more equations with the same variables is called system of equations.

Explanation of Solution

Given information:

The given statement:

The set of two or more inequalities with the same variables is called system of equations.

Concept used:

The inequality is mathematical expression of the form $x+2y\ge 7$ or $x+2y\le 7$ .

An equation is a mathematical expression whose left hand side is equal to the right hand side numerically. For example the expression $x+2y=7$ is an equation in the variables x and y.

A set of equations in common variables is called the “system of equations”.

The set of equations $S=\left\{x+2y=7,2x-y=4,\text{where}x,y\text{are}\text{real}\text{numbers}\right\}$ is called system of equations. There is no involvement of any inequality

Thus, the given statement is false.

The true statement is:

The set of two or more equations with the same variables is called system of equations.

Conclusion:

The given statement is false.The true statement is:

The set of two or more equations with the same variables is called system of equations.