Linear equations are one degree equations having the exponent on the variable one.

Working on linear algebra, we must have come across many algebra equations. These expressions have one, two or more variables. In this section will study about how to write standard equations for linear equations with variable one, two and three along with the help of some solved examples. After practice below listed problems, you will be ready to convert any equation into standard from at our own pace.

An equation consists of real numbers and multiple of a variable. A linear equation with one variable is a first-degree equations because the exponent on the variable is always 1. Solution for such equations be always a value which satisfy the given equation. For the above equation, x = -B/A is the required result.

This is the standard form of linear equations in one variable :

Ax + B = 0

Where A, and B are all real numbers and A can not be zero.

This is the standard form of linear equations in one variable :

Ax + B = 0

Where A, and B are all real numbers and A can not be zero.

Often when we deal with questions based on linear question, the very first question arise in our mind is, What is the linear standard form? The standard form of linear equations in two variables:

Ax + By = C

Where A, B And C are all real numbers and A and B can not be zero.

We can graph such equations in xy plane after finding the x-intercept and y-intercepts of the corresponding equation. For example, if we are given with the equation 2x - y = 10 then

**Graph will looks like**:

We can graph such equations in xy plane after finding the x-intercept and y-intercepts of the corresponding equation. For example, if we are given with the equation 2x - y = 10 then

To Find x-intercept | Set y = 0 | 2x - y = 10 2x = 10 x = 5 |
x-intercept = (5, 0) |

To Find y-intercept | Set x = 0 | 2(0) - y = 10 - y =10 y = -10 |
y-intercept = (0, -10) |

Ax + By + Cz = D

Where A, B, C and D are all real numbers and A, B and C can not be zero.

Since this equation contains 3 variables, so we need 3 more similar equations to find the values of x, y and z. Mostly matrix method helps to get the result.

Given equation is 3x - 10y = 30

Set value of x as zero

3 $\times$ 0 - 10 y = 30

- 10y = 30

Divide each side by -10

$\frac{-10y}{-10}$ = $\frac{30}{-10}$

y = -3

Set value of y as zero

3x - 10 $\times$ 0 = 30

3x - 0 = 30

3x = 30

Dividing both sides by 3

3x/3 = 30/3

x = 10

x-intercept is (10, 0)

y-intercept is (0, -3)

Given equation is y = 3x/11 + 10

As above linear equation consists two variables x and y, it shows this is a linear equations with two variable.

So convert given equation into its standard from which is ax + by + c = 0.

Now:

Reduce the fraction

y = 3x/11 + 10

Multiply each side by 11

11(y = 3x/11 + 10)

11y = 11 $\times$ 3x/11 + 11 $\times$ 10

11y = 3x + 110

11y - 3x - 110 = 0

or -3x + 11y - 110 = 0

Which is the required result.

-3x + 11y - 110 = 0 similar to ax + by + c = 0, where a = -3, b = 11 and c = -110

Problem 1:

a) x(1/2 - 3) + 2(x-4) = 0

b) 3x- 4(y + 2) - 1/2(z - x - y) + 13 = 0

c) 9y/5 + 5(x - y + 2) - 11/5 = 0