 Hello and welcome to the session let's work out the following problem it says solve the following system of linear equations graphically given equations are 5x-6y plus 30 is equal to 0 and 5x plus 4y minus 20 is equal to 0 also find the vertices of the triangle formed by the two lines and the x-axis so let's now move on to the solution now the first equation is 5x minus 6y plus 30 is equal to 0 and this can be written as 5x minus 6y is equal to minus 30 now to draw the graph of this equation we need to make a table which gives us the points through which the graph passes through so now if we put x is equal to 0 equation will become 0 minus 6y is equal to minus 30 so y is equal to minus 30 upon minus 6 that is 5 now if we put y is equal to 0 the equation will become 5x minus 0 is equal to minus 30 so x will be equal to minus 30 upon 5 that is 6 now if we put x is equal to 1 the equation will become 5 minus 6y is equal to minus 30 that means minus 6y is equal to minus 30 minus 5 so this implies y is equal to minus 35 upon minus 6 dividing minus 35 by minus 6 we have answer as 5.8 so y will be 5.8 and here x will be minus 6 now we draw the graph of the equation 5x minus 6y is equal to minus 30 when x is 0 y is 5 this is the point 0 5 when y is 0 x is minus 6 here y is 0 and x is minus 6 this point is minus 6 0 and when x is 1 y is 5.8 x is 1 y is 5.8 so joining these three points we have a line 5x minus 6y is equal to minus 30 now the second equation is 5x plus 4y is equal to 20 it can be written as 5x plus 4y is equal to 20 now we make a table now when x is 0 the equation will become 0 plus 4y is equal to 20 that is 4y is equal to 20 that is y is equal to 20 by 4 that is 5 and if y is 0 equation will become 5x plus 0 is equal to 20 that is 5x is equal to 20 that is x is equal to 5 upon 20 upon 5 that is 4 now if we take y as 1 so the equation will be 5x plus 4 is equal to 20 so this implies 5x is equal to 20 minus 4 that is 16 so this implies x is equal to 16 upon 5 dividing 16 by 5 it gives us 3.2 now we draw the graph of the equation 5x plus 4y is equal to 20 now when x is 0 y is 5 that is this point again when y is 0 x is 4 that is this point this is 4 0 and when x is 1 y is 3.2 that is here now we join these three points to get the graph of this equation this is the line 5x plus 4y is equal to 20 now we have to find the vertices of the triangle formed by these two lines and the x-axis now these are the two lines and this is the x-axis and we name this triangle as triangle ABC and we see that the vertices of the triangle are 0 5 minus 6 0 and 4 0 so A has coordinate 5 0 coordinate of the point B or the vertex of the triangle ABC is minus 5 0 that is minus 6 0 and point C has coordinates 4 0 so this completes the question and the session by for now take care have a good day.