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subject: Multivariable Linear Equations [print this page]

Linear equation is one of a method for problem in algebra. Linear equation is in three types. That is single variable, two variables and three variables. Multi variable linear equation is a more than one variable equation. In online few websites are providing linear equation tutoring. In this article we shall discuss for multivariable linear equations.

Sample Problem for Multivariable Linear Equations:

Multivariable linear equations questions 1:

Evaluate the given multivariable equation and find out x and y value of the equation.

11x + 3y 14 = 0

-11x + 12y 1 = 0

Solution:

We are going to find out the x and y value of the given algebra 1 linear equation.

11x + 3y = 14

-11x + 12y = 1

In the first we are going to add equation (1) and (2). We get

11x + 3y = 14

-11x + 12y = 1

0x + 15y = 15

y = 1

Now, we get the y value as 1. In the equation (2) we substitute y = 1, we get

-11x + 12(1) = 1

-11x + 12 = 1

-11x = -11

x = 1

Now, we get the x value as 1. So, the given multivariable of linear equation values are x = 1, y = 1.

Multivariable Linear Equations Questions 2:

Evaluate the given multivariable equation and find out x and y value of the equation.

6x + 5y 11 = 0

-6x + 8y 2 = 0

Solution:

We are going to find out the x and y value of the given algebra linear equation.

6x + 5y = 11

-6x + 8y = 2

In the first we are going to add equation (1) and (2). We get

6x + 5y = 11

-6x + 8y = 2

0x + 13y = 13

y = 1

Now, we get the y value as 1. In the equation (2) we substitute y = 1, we get

-6 + 8(1) = 2

-6x + 8 = 2

-6x = -6

x = 1

Now, we get the x value as 1. So, the given multivariable of linear equation values are x = 1, y = 1.

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.

Standard form of linear equation:

A x + B y=C. where A, B, and C are integers whose greatest common factor is 1, A and B are not both equal to zero, and A is non-negative (and if A = 0 then B has to be positive).

Slope intercept form of Linear equations:

A common form of a linear equation in the two variables x and y is

y = m x + b. Where, m and b designate constants.

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Parallel Linear equation:

Any two linear equations, the coefficients of x and y are identical in value and sign, then these two equations are parallel.

It is also defined as the parallel lines having the slopes are equal.

Example Problems on Linear Equation Parallel

Example problem 1:

Find the equation of a line parallel to the equation 3x - y - 2 = 0 and passing through the point (4, 2).

Solution:

Let us take the equation is 3x - y +C= 0

Substitute the (x, y) = (4, 2) in the equation 3x-y-2=0

3(5) - (2) + C = 0

C= -13

Thus, the required equation is

3x -y- 13 =0

This is the equation of a line parallel to 3x - y - 2 = 0.

Linear parallel

Additional Problems:

mple problem 2:

Determine if the given lines are parallel:

y = 2x+5

-2x+y = -2

Solution:

y = 2x+5-----------Equation (1)

-2x+y = -2 ---------- Equation (2)

From equation (1)

Comparing y=2x+5 with the Basic slope intercept form y=mx+b.

So,the slope is 2

From equation (2)

Add 2x on both sides

-2x+y+2x=-2+2x

y=2x-2

Comparing y=2x-2 with the Basic slope intercept form y = mx+b.

So,the slope is 2.

Both the lines have the same slope. So, the given two lines are parallel.

Linear parallel

Example problem 3:

Determine whether the given lines are parallel or not:

y = 3x+8

-3x+y = -8

Solution:

y = 3x+8-----------Equation (1)

-3x+y = -8 ---------- Equation (2)

From equation (1)

The slope is 3

From equation (2)

Add 3x on both sides

-3x+y+3x=-8+3x

y=3x-8

The slope is 3.

Both the lines have the same slope. So, the given two lines are parallel.

by: mathqa

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