Table of Contents
Pair of Linear Equations in Two Variables Graphical Method
Graph the linear equations in two variables given by y = mx + b and y = -3x + c.
The linear equations in two variables are y = mx + b and y = -3x + c.
The graph of y = mx + b is a straight line with slope m and y-intercept b.
The graph of y = -3x + c is a straight line with slope -3 and y-intercept c.
How to solve the Pair of Linear equations?
To solve the pair of linear equations, we will use the substitution method.
We will start by solving the first equation for y.
y = 2x – 1
Next, we will substitute this value for y into the second equation.
2x – 1 = 3
We will then solve for x.
x = 2
Representation
of a Binary Tree
A binary tree is a data structure that allows two nodes to be linked together by a path from the root to the leftmost child, and from the leftmost child to the rightmost child. The path is called a path from the root to the leftmost child, and from the leftmost child to the rightmost child. The path is called a path from the root to the leftmost child, and from the leftmost child to the rightmost child. The path is called a path from the root to the leftmost child, and from the leftmost child to the rightmost child.
Graphical Representation
of the Grid
The grid is shown below. The shaded region represents the space that the cat can move.
The grid is shown below. The shaded region represents the space that the cat can move.
Algebraic Representation
of Points
A point can be represented algebraically as a coordinate pair in terms of a Cartesian coordinate system. In a Cartesian coordinate system, points are located by their x-coordinate and y-coordinate. The x-coordinate is the distance from the origin to the point along the x-axis, and the y-coordinate is the distance from the origin to the point along the y-axis.
Solving the Pair of Linear Equation in Two Variables
There are three methods to solving a pair of linear equations in two variables: substitution, elimination, and graphing.
1. Substitution Method
The substitution method is a way of solving a pair of linear equations in two variables by substituting one equation into the other.
For example, consider the equations
x + y = 5
2x – y = 3
The substitution method can be used to solve for either x or y. In this example, we will solve for x.
To solve for x, we substitute the equation x + y = 5 into the equation 2x – y = 3.
2x – y = 3
x + y = 5
3 = 2x
x = 3
Pair of Linear Equations in Two Variables Graphical Method
The graphical method is a way of solving a pair of linear equations in two variables by graphing the equations and then finding the point of intersection of the graphs.
To graph a pair of linear equations in two variables, first plot the coefficients of the x-variable on the x-axis and the coefficients of the y-variable on the y-axis. Then, draw a line through the points representing the equations. The point of intersection of the two lines is the solution to the equations.
Substitution Method:
To find the value of x in the equation
3x + 5 = 7
we use the substitution method. We know that the value of x is 5, so we substitute 5 for x in the equation.
3x + 5 = 7
3(5) + 5 = 7
15 + 5 = 7
20 = 7
The value of x is 20.
Elimination Method:
We can solve this equation using the elimination method.
We will start by multiplying each equation by 2.
2x + 3y = 6
2x + 6y = 12
We will then subtract the second equation from the first equation.
2x + 3y = 6
-2x + 6y = 12
We will then add 3y to each side.
0 = 3y
y = 0
Cross-Multiplication Method:
To multiply two matrices, the cross-multiplication method is used. In this method, the products of the corresponding entries in the two matrices are multiplied together.
For example, to multiply the matrices:
\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}
\begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}
we would multiply the corresponding entries in the two matrices:
1 x 5 = 5
2 x 7 = 14
3 x 6 = 18
4 x 8 = 32
Adding these together gives us the result:
105
