 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that Solve the following system of equations graphically and the equations given are y is equal to minus of x square plus 4x plus 1 and y is equal to 3x minus 1. Let us start with the solution of the given question. We are given the following system of equations and we mark this equation as equation number 1 and this equation as equation number 2. We have to solve this quadratic linear system of equations graphically. First we will graph both these equations on the coordinate plane. First we take this quadratic equation. It is a parabola of the form y is equal to ax square plus bx plus c and its axis of symmetry is given by the equation x is equal to minus of b upon 2a. So on comparing these two equations we get the axis of symmetry of the given equation as x is equal to minus b. Now we know that b which is the coefficient of x is 4 so minus b will be equal to minus of 4 upon 2 into a. Now a is coefficient of x square which is equal to minus 1 so we have 2 into minus 1 which implies that x is equal to minus 4 upon minus 2 which is equal to 2. So the axis of symmetry of the given equation is given by x is equal to 2. So first on the coordinate plane we draw the axis of symmetry given by the equation x is equal to 2. So at x is equal to 2 we draw a vertical line. This vertical line represents axis of symmetry given by the equation x is equal to 2. Now we will make table of values for this equation that is y is equal to minus of x square plus 4x plus 1. Now if we put the value of x as minus 1 we get the value of y is equal to minus of minus 1 whole square plus 4 into minus 1 plus 1 which implies that y is equal to minus of 1 minus 4 plus 1 which further implies that y is equal to minus 4. So for x is equal to minus 1 y is equal to minus 4. Similarly for x is equal to 0 y is equal to minus of 0 square plus 4 into 0 plus 1 which implies that y is equal to minus of 0 square is 0 plus 4 into 0 is 0 that is plus 0 plus 1 which implies that y is equal to 1. So for x is equal to 0 the value of y is 1. Similarly for x is equal to 1 y is equal to 4. For x is equal to 2 the value of y is 5. For x is equal to 3 y is equal to 4. For x is equal to 4 the value of y is 1 and for x is equal to 5 y is equal to minus 4. Now we shall plot all these points on the coordinate plane. Now we have plotted all these points on the coordinate plane and we join these points by drawing a free hand curve keeping in mind the axis of symmetry so that the curve is equidistant from the line of symmetry from both the sides. The equation of the curve is y is equal to minus of x square plus 4x plus 1. We see that it is a downward facing parabola. Now we draw graph of the equation y is equal to 3x minus 1. It is the equation of a straight line. Let us make it stable of values. Now we have when x is equal to 0 y is equal to 3 into 0 minus 1 which implies that y is equal to 0 minus 1 that is equal to minus 1. So for x is equal to 0 y is minus 1. When we take the value of x as 1 the value of y is equal to 3 into 1 minus 1 which implies that y is equal to 3 minus 1 that is equal to 2. So for x is equal to 1 y is equal to 2 and if we put the value of x as 2 we get the value of y as 3 into 2 minus 1 which implies that y is equal to 6 minus 1 that is equal to 5. So for x is equal to 2 y is equal to 5. Now we plot these ordered pairs on the coordinate plane. So now we have plotted these points on the coordinate plane. Now we have joined these points and we have obtained the straight line which represents the graph of the equation y is equal to 3x minus 1. Now from this graph we see that this straight line intersects the parabola at two points and these two points are here this point with coordinates minus 1 minus 4 and this point with coordinates 2 5. Let us name these points as A and B. Thus the solution set of the system is the set containing ordered pairs minus 1 minus 4 to 5. This is the required answer. This completes our session. Hope you enjoyed this session.