Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations by the substitution method: \[ 11x + 15y + 23 = 0 \\ , 7x – 2y – 20 = 0 \] Solution Step 1: Write the Equations in Standard Form \[ 11x + 15y = -23 […]
Solve the following systems of equations: 11x+15y+23=0, 7x-2y-20=0 Read More »
Graphical Solution and Area of Triangles with the X-Axis Video Explanation Question Draw the graphs of the pair of linear equations: \[ x – y + 2 = 0 \] \[ 4x – y – 4 = 0 \] Calculate the area of the triangles formed by the lines so drawn and the x-axis. Solution
Graph of Lines and Area of the Figure Formed Video Explanation Question Draw the graphs of the lines \(x = -2\) and \(y = 3\). Write the vertices of the figure formed by these lines, the x-axis and y-axis. Also, find the area of the figure. Solution Step 1: Description of the Given Lines The
Graph of Linear Equations and Area of the Quadrilateral Video Explanation Question Draw the graph of the equations: \[ x = 3 \] \[ x = 5 \] \[ 2x – y – 4 = 0 \] Also find the area of the quadrilateral formed by these lines and the x-axis. Solution Step 1: Write
Graphical Determination of the Vertices of a Triangle Video Explanation Question Determine graphically the vertices of the triangle formed by the lines: \[ y = x \] \[ 3y = x \] \[ x + y = 8 \] Solution Step 1: Write the Equations in Convenient Form Equation (1): \(y = x\) Equation (2):
Graphical Solution and Ratio of Areas of Triangles Video Explanation Question Graphically solve the following pair of equations: \[ 2x + y = 6 \] \[ 2x – y + 2 = 0 \] Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and
Graphical Determination of the Vertices of a Triangle Video Explanation Question Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are: \[ y = x \] \[ 3y = x \] \[ x + y = 8 \] Solution Step 1: Write the Equations in Convenient Form Equation (1):
Graphical Determination of the Vertices of a Triangle Video Explanation Question Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are: \[ y = x \] \[ y = 2x \] \[ y + x = 6 \] Solution Step 1: Write the Equations in Convenient Form Equation (1):
Different Geometrical Representations of a Pair of Linear Equations Video Explanation Given Equation The given linear equation is: \[ 2x + 3y – 8 = 0 \] Solution (i) Intersecting Lines For two lines to intersect, their coefficients must satisfy: \[ \frac{a_1}{a_2} \ne \frac{b_1}{b_2} \] Choose another equation such as: \[ x + y –
Graphical Representation of a Pair of Linear Equations Video Explanation Question Represent the following pair of equations graphically and write the coordinates of the points where the lines intersect the y-axis: \[ x + 3y = 6 \] \[ 2x – 3y = 12 \] Solution Step 1: Write Both Equations in the Form \(y