 Hi and welcome to the session. Let's work out the following question. The question says solve the following system of linear equations graphically 3x minus 5y equals to 19 is the first equation and 3y minus 7x plus 1 equal to 0 is the second one Does the point 49 lie on any of the lines write its equation So let's start with the solution to this question Now equation of the first line is 3x minus 5y equals to 19 This implies 5y is equal to 9 3x minus 19 and this implies that y is equal to 3x minus 19 divided by 5 now equation of the other line is 3y minus 7x plus 1 is equal to 0 This implies 3y is equal to 7x minus 1 and this implies that y is equal to 7x minus 1 divided by 3 Now let us find the points lying on this line The points will be When we take x to be equal to 4 we get y as minus 1.4 when we take x to be 7 Y is 0.4 when x is minus 2 y is minus 5 Similarly for this line the three points lying on this line are When x is 1 y is 2 when x is minus 2 y is minus 5 and x is 4 y is 9 So let us plot these points on the graph and make these two lines now on solving these two equations we get The point of intersection as minus 2 minus 5 Because we see that when we solve 3x minus 5 y equal to 19 and minus 7x plus 3 y equal to minus 1 we get x as Minus 2 and y as minus 5 So our answer to first part is Minus 2 minus 5 Also the question says does the point for 9 lie on any of the lines so on the line 3 y minus 7x plus 1 equal to 0 Let us put x to be 4 y equal to 9 we get the left hand side as 3 into 9 minus 7 into 4 plus 1 This is equal to 27 minus 28 plus 1 and that is equal to 0 that is also equal to the RHS of the given equation Therefore we can say that yes the point 4 9 Lies on 3x minus Sorry, this is 3 y minus 7 x plus 1 equal to 0 So this is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day