Table of Contents
Pair of Linear Equation
A linear equation is an equation in which each term is a constant multiple of the first term. Linear equations can be written in slope-intercept form, standard form, or point-slope form.
A pair of linear equations is a set of two linear equations that are solved simultaneously. The equations are written in slope-intercept form and are graphed on the same coordinate plane. The point of intersection of the two graphs is the solution to the pair of equations.
Pair of Linear Equation in Two variables Introduction
A linear equation in two variables is an equation that can be written in the form y = mx + b, where m and b are constants. This type of equation can be used to model a linear relationship between two variables.
For Example
In general, the use of a pronoun can refer back to a noun earlier in the text. For example, in the sentence “John is taller than any other student in the class,” the pronoun “he” refers back to the noun “John.” Pronouns can also be used to avoid repetition of a noun. For example, in the sentence “John is taller than any other student in the class, and he is also the captain of the basketball team,” the pronoun “he” is used to avoid repeating the noun “John.”
Expression of Pair of Linear Equation in Two Variables
If a and b are two real numbers, then the equation
a + b = 0
represents a pair of linear equations in two variables.
Graphical Expression of Pair of Linear Equation in Two Variables
The graphical expression of a pair of linear equations in two variables is a line graph.
Algebraic Method of Solving a Pair of Linear Equations of Two Variables.
To solve a pair of linear equations in two variables using the algebraic method, we use the following steps:
1. Solve one of the equations for one of the variables.
2. Substitute the value of the variable from the first equation into the second equation.
3. Solve the equation for the other variable.
4. Check the solutions to make sure they work in both equations.
Let’s solve the following pair of linear equations in two variables:
2x + 3y = 5
2x – 3y = -4
Step 1: Solve one of the equations for one of the variables. We will solve the equation 2x + 3y = 5 for y.
y = 5 – 2x
Step 2: Substitute the value of y from the first equation into the second equation.
2x – 3(5 – 2x) = -4
2x – 15 + 3x = -4
-13x = -19
x = 1.46
Step 3: Solve the equation for the other variable. We will solve the equation 2x – 3y = -4 for x.
x = -4 + 3y
Step 4: Check the solutions to make sure they work in both equations.
2x + 3y = 5
2x – 3y = -4
What is a Linear equation?
A linear equation is an equation in which each term is linear.
How to Solve the Pair of Linear Equations?
There are a few steps in solving a pair of linear equations. The first step is to clear the fractions and decimals from the equations. Next, combine like terms on each side of the equation. Lastly, solve for the unknown variable.
For this problem, the equations are:
x + 2y = 3
4x – 5y = -11
To clear the fractions and decimals, divide each side of the equation by the coefficient of the variable.
x + 2y = 3
4x – 5y = -11
x + 2y = 3
4x – 5y = -11
x + 2y = 3
4x – 5y = -11
Next, combine like terms on each side of the equation.
x + 2y = 3
4x – 5y = -11
x + 2y = 3
9x = -8
Lastly, solve for the unknown variable.
x = -8/9
Representation
Representative democracy is a form of government in which people elect representatives to make decisions on their behalf. The representatives are elected by the people they represent.
