Pair of Linear Equations in Two Variables

About Pair of Linear Equations in Two Variables Notes

A pair of linear equations in two variables is a system of two equations in two variables. A system of equations is a set of equations that are solved together.

The two equations in a pair of linear equations are usually written in the form:

ax + by = c

dx + ey = f

where a, b, c, d, and e are constants. The variables x and y are the unknowns that we are trying to solve for.

There are a few things that we can do to solve a pair of linear equations:

-Add the equations together.

-Subtract the equations.

-Multiply one of the equations by a constant.

-Divide one of the equations by a constant.

Once we have solved for the unknowns, we can graph the solutions on a coordinate plane.

Pair of Linear Equations in Two Variables Solutions

A linear equation in two variables is an equation that can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

There are many methods for solving linear equations in two variables, including graphing, substitution, and elimination.

The most common method for solving linear equations is to use the algebraic method of elimination. In this method, the equations are rewritten so that the variables are on one side of the equation and the constants are on the other side. The variables are then eliminated by adding or subtracting the equations.

For example, consider the equation y = 2x + 3.

This equation can be rewritten as y – 2x = 3.

The variables can then be eliminated by adding the equations.

y + y – 2x = 3 + 3

2y = 6

y = 6

Important Terms Related to Pair of Linear Equations in Two Variables Examples

System of equations: A system of equations is a set of two or more equations that are solved simultaneously.

Solution: The solution to a system of equations is the set of values that makes each equation in the system true.

Variable: A variable is a letter that represents an unknown quantity in an equation.

Representing a Pair of Linear Equations in Two Variables

There are several ways to represent a pair of linear equations in two variables.

One way is to use a table to organize the information.

Another way is to use a graph to visually represent the information.

(image to be added soon)

The Apollo 12 mission, launched on November 14, 1969, was the second manned mission to the Moon and the sixth manned mission of the Apollo program. It was the fourth manned mission to land on the Moon. The mission was commanded by Charles “Pete” Conrad and piloted by Richard F. Gordon. Alan Bean, the lunar module pilot, became the fourth human to walk on the Moon.

The primary objectives of the Apollo 12 mission were to explore the Ocean of Storms region of the Moon, to deploy the Apollo Lunar Surface Experiments Package (ALSEP), and to obtain samples of lunar material. The mission was successful, meeting all primary objectives.

The Apollo 12 mission was the first to use the lunar roving vehicle. The mission also achieved the first successful double rendezvous in space, docking the Apollo Command/Service Module (CSM) with the Apollo Lunar Module (LM) after the LM had been separately launched hours earlier.

The Apollo 12 mission was the first to visit the Surveyor 3 spacecraft, which had landed on the Moon two and a half years earlier. The mission retrieved parts of the Surveyor 3 camera and other equipment.

The Apollo 12 mission was also the first to visit the Moon’s South Pole.

The Apollo 12 mission was the second manned mission to land on the Moon and the sixth manned mission of the Apollo program. It was the fourth manned mission to land on the Moon.

Methodology of Solving a Pair of Linear Equations

There are a few different methods that can be used to solve a pair of linear equations. The most common methods are substitution and elimination.

Substitution Method

In the substitution method, one of the equations is solved for one of the variables, and that value is then substituted into the other equation. The equation is then solved to find the other variable.

For example, let’s say that we are solving the equations 2x = 3 and x + 4 = 7. We can solve the first equation for x, and we get x = 3. We can then substitute 3 for x in the second equation and solve for y. We get y = 3.

Elimination Method

In the elimination method, one of the equations is solved for one of the variables, and that value is then substituted into the other equation. The equation is then solved to find the other variable.

For example, let’s say that we are solving the equations 2x = 3 and x + 4 = 7. We can solve the first equation for x, and we get x = 3. We can then substitute 3 for x in the second equation and solve for y. We get y = -1.

Elimination Method

The elimination method is a way to solve systems of linear equations.

To solve a system of linear equations using the elimination method, we will

1. Add the equations together to get rid of the variable

2. Solve the equation that remains

3. Substitute the value we found in step 2 into one of the original equations

4. Solve for the variable

5. Check our work

Here is an example:

Solve the system of linear equations using the elimination method:

3x + 2y = 5

2x – y = 1

We will add the equations together to get rid of the variable:

5x = 6

We will solve the equation that remains:

x = 6/5

We will substitute the value we found in step 2 into one of the original equations:

3x + 2y = 5

3x + 2(6/5) = 5

3x + 12 = 5

x = -7

We will solve for the variable:

3x + 2y = 5

3x + 2(-7) = 5

3x – 14 = 5

We will check our work:

3x + 2y = 5

3x + 2(-7) = 5

3x – 14 = 5

3x – 2

Cross Multiplication Method

The cross multiplication method is a way of solving equations with variables on both sides.

To use the cross multiplication method, you need to find a number that will work on both sides of the equation. This number is called a multiplier.

Once you have found the multiplier, you can use it to solve the equation.

To use the cross multiplication method, follow these steps:

1. Multiply the coefficients of the variable on each side of the equation.

2. Divide each side of the equation by the multiplier.

3. Solve the equation.

Here is an example:

3x = 12

3x ÷ 3 = 12 ÷ 3

x = 4

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