 Hello and welcome to the session. The given question says, solve the following system of linear equations graphically. The given equations are 4x minus 5y minus 20 is equal to 0 and 3x plus 5y minus 15 is equal to 0. Determine the vertices of the triangle formed by the lines representing the above equation and the y-axis. So let's start with the solution and the given equations are first is 4x minus 5y minus 20 is equal to 0. Let this be equation number 1 and the second one is 3x plus 5y minus 15 is equal to 0. Let this be equation number 2. To solve the given problem graphically first let us find the values of x and y with satisfy equation 1. So from 1 we have 4x is equal to 20 plus 5y or x is equal to 20 plus 5y divided by 4. Now let us make a table and which we should jot down the values of x and y. Now when y is 0 then x is 20 divided by 4 which is equal to 5. When x is 0 then we have 20 plus 5y is equal to 0. So this implies 5y is equal to minus 20 which gives that y is equal to minus 4 and when let us take y as minus 2 so when y is minus 2 then x is equal to 10 divided by 4 which is equal to 2.5. So this solves the first equation. Now let us find the values of x and y with satisfy the second equation. Now from the second equation we have 5y is equal to 15 minus 3x or y is equal to 15 minus 3x divided by 5. Again let us make a table and write down the values of x and y with satisfy this equation. Now when x is 0 then y is 15 divided by 5 which gives 3 and when y is 0 then we have 15 minus 3x is equal to 0. So x is equal to 15 divided by 3 which is equal to 5 and when we suppose x as 2 then y is equal to 9 divided by 5 which is 1.8. Now let us plot these two equations on the graph starting with the first one. When x is 5 y is 0 so this point denotes 5 0 when x is 0 y is minus 4 this point denotes 0 minus 4 and when x is 2.5 y is minus 2. So here when x is 2.5 which is around somewhere around this point y is minus 2 so this point denotes 2.5 comma minus 2. Now let us join these three points to get the graph of first equation. So this is the graph of line 4x minus 5 y minus 20 is equal to 0. Now let us plot the points and the second table when x is 0 y is 3 so this point denotes 0 3 and when x is 5 y is 0 so this point denotes 5 0 as this point is already line 1 so this point is common to both the lines and the third point is when x is 2 y is 1.8 so this point denotes 2 comma 1.8. Now let us join these three points to get the graph of the second equation. So this is the graph of equation 3x plus 5 y minus 15 is equal to 0. Now we have to determine the vertices of the triangle formed by the lines representing the above equations and the y axis. So this is the region which is determined by the two lines and the y axis. So this is the required triangle. Now we have to determine its vertices so its vertices are this point which is 0 3 that is denoted by p this point which is 5 0 denoting it by q and this point denoting it by r which is 0 comma minus 4. Therefore p q and r are the vertices of the required triangle formed by the given lines and the y axis. Hence our answer is vertices of triangle p q r r p with coordinates 0 3 q with coordinates 5 0 and r with coordinates 0 comma minus 4. So this completes the session. Hope you have understood it. Bye and take care.