Chapter 3: Q65. (page 122)

Write each equation in standard form. Identify A, B, and C.
$\frac{2}{3} y - 6 = 1 - x$

Short Answer

Expert verified

The standard form of the equation is $3 x + 2 y = 21$ and localid="1647606012634" $A = 1, B = 2, C = 6$ .

Step by step solution

Step-1 – Apply the concept of Standard form of equation

Any linear equation with variables xand ycan be expressed in the standard form as:

$A x + B y = C$

Where A, B, and C are all integers with greatest common factor as 1.

Step-2 – Convert the equation into standard form

Consider the given equation.

$\frac{2}{3} y - 6 = 1 - x$

To convert it into standard form, add x and 6on both sides of equation.

$\begin{matrix} \frac{2}{3} y - 6 + x + 6 = 1 - x + x + 6 \\ x + \frac{2}{3} y = 7 \end{matrix}$

Now, multiply whole equation by $3$ .

$\begin{matrix} (3) (x + \frac{2}{3} y) = (3) (7) \\ 3 x + 2 y = 21 \end{matrix}$

Thus, the standard form of the equation is $3 x + 2 y = 21$ .

Step-3 – Identification of A, B, and C

Comparing $3 x + 2 y = 21$ with standard form $A x + B y = C$ , we get

$\begin{array}{l} A = 3 \\ B = 2 \\ C = 21 \end{array}$

Hence, the standard form of the equation is $3 x + 2 y = 21$ and $A = 3, B = 2, C = 21$ .

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Write each equation in standard form. Identify A, B, and C.
$\frac{2}{3} y - 6 = 1 - x$

Short Answer

Step by step solution

Step-1 – Apply the concept of Standard form of equation

Step-2 – Convert the equation into standard form

Step-3 – Identification of A, B, and C

One App. One Place for Learning.

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Write each equation in standard form. Identify A, B, and C. 23y-6=1-x

Short Answer

Step by step solution

Step-1 – Apply the concept of Standard form of equation

Step-2 – Convert the equation into standard form

Step-3 – Identification of A, B, and C

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Geometry

Statistics

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Write each equation in standard form. Identify A, B, and C.
$\frac{2}{3} y - 6 = 1 - x$