Chapter 7, Problem 1TYWP

See how well you have learned the vocabulary in this chapter.

A linear equation in two variables is an equation that can be written in the form

A. $Ax+By<C$

B. $ax=b$

C. $y=x^2$

D. $Ax+By=C$

To determine

The form of a linear equation in two variables from the provided options.

A. $Ax+By<C$

B. $ax=b$

C. $y=x^2$

D. $Ax+By=C$

Answer to Problem 1TYWP

Solution:

The correct form of a linear equation in two variables is $\underset{\_}{\left(D\right)Ax+By=C}$.

Explanation of Solution

Given Information:

For writing a linear equation in two variables, the options are:

A. $Ax+By<C$

B. $ax=b$

C. $y=x^2$

D. $Ax+By=C$

A linear equation in two variables is an equation that can be written in the form.

$Ax+By=C$

Where A, B, and C are real numbers and A and B are not both $0$. This form is called standard form.

Examples:

$3x+4y=9,x+2y=-8$

Therefore, a linear equation in two variables can be written in the form $Ax+By=C$.

A. Consider the expression $Ax+By<C$.

The expression does not match with the given statement because an equation has something on the left side, an = symbol, and something on the right side while this option is not an equation.

Therefore, the option A is incorrect.

B. Consider the expression $ax=b$.

The expression does not match with the given statement because in the given statement standard form of a linear equation in two variables has been asked while this option has only one variable.

Therefore, the option B is incorrect.

C. Consider the expression $y=x^2$

The expression does not match with the given statement because $y=x^2$ is the equation of parabola and not a linear equation in two variables.

Therefore, the option C is incorrect.

D. Consider the expression $Ax+By=C$.

The expression matches with the given statement because this option is an equation with two variables and non-zero constants.

Therefore, the option D is correct.

Therefore, the correct form of a linear equation in two variables is $\left(D\right)Ax+By=C$.