Page 1 Exercise – 3A 1. Solve the system of equations graphically: 2x + 3y = 2, x – 2y = 8 Sol: On a graph paper, draw a horizontal line X'OX and a vertical line YOY' representing the x- axis and y-axis, respectively. Graph of 2x + 3y = 2 2x + 3y = 2 ?3y = (2 – 2x) ?3y = 2(1 – x) ?y = ?? (?? -?? ) ?? …(i) Putting x = 1, we get y = 0 Putting x = -2, we get y = 2 Putting x = 4, we get y = -2 Thus, we have the following table for the equation 2x + 3y = 2 x 1 -2 4 y 0 2 -2 Now, plot the points A(1, 0), B(-2, 2) and C(4, -2) on the graph paper. Join AB and AC to get the graph line BC. Extend it on both ways. Thus, the line BC is the graph of 2x + 3y = 2. Graph of x - 2y = 8 x – 2y = 8 ? 2y = (x – 8) ? y = ?? -?? ?? …(ii) Putting x = 2, we get y = -3 Putting x = 4, we get y = -2 Putting x = 0, we get y = -4 Thus, we have the following table for the equation x – 2y = 8. x 2 4 0 y -3 -2 - 4 Now, plot the points P(0, -4) and Q(2, -3). The point C(4, -2) has already been plotted. Join PQ and QC and extend it on both ways. Thus, line PC is the graph of x – 2y = 8. Page 2 Exercise – 3A 1. Solve the system of equations graphically: 2x + 3y = 2, x – 2y = 8 Sol: On a graph paper, draw a horizontal line X'OX and a vertical line YOY' representing the x- axis and y-axis, respectively. Graph of 2x + 3y = 2 2x + 3y = 2 ?3y = (2 – 2x) ?3y = 2(1 – x) ?y = ?? (?? -?? ) ?? …(i) Putting x = 1, we get y = 0 Putting x = -2, we get y = 2 Putting x = 4, we get y = -2 Thus, we have the following table for the equation 2x + 3y = 2 x 1 -2 4 y 0 2 -2 Now, plot the points A(1, 0), B(-2, 2) and C(4, -2) on the graph paper. Join AB and AC to get the graph line BC. Extend it on both ways. Thus, the line BC is the graph of 2x + 3y = 2. Graph of x - 2y = 8 x – 2y = 8 ? 2y = (x – 8) ? y = ?? -?? ?? …(ii) Putting x = 2, we get y = -3 Putting x = 4, we get y = -2 Putting x = 0, we get y = -4 Thus, we have the following table for the equation x – 2y = 8. x 2 4 0 y -3 -2 - 4 Now, plot the points P(0, -4) and Q(2, -3). The point C(4, -2) has already been plotted. Join PQ and QC and extend it on both ways. Thus, line PC is the graph of x – 2y = 8. The two graph lines intersect at C(4, -2). ? x = 4 and y = -2 are the solutions of the given system of equations. 2. Solve the system of equations graphically: 3x + 2y = 4, 2x – 3y = 7 Sol: On a graph paper, draw a horizontal line X'OX and a vertical line YOY' representing the x- axis and y-axis, respectively. Graph of 3x + 2y = 4 3x + 2y = 4 ?2y = (4 – 3x) ?y = ?? - ???? ) ?? …(i) Putting x = 0, we get y = 2 Putting x = 2, we get y = -1 Putting x = -2, we get y = 5 Thus, we have the following table for the equation 3x + 2y = 4 x 0 2 -2 y 2 -1 5 Now, plot the points A(0, 2), B(2, -1) and C(-2, 5) on the graph paper. Join AB and AC to get the graph line BC. Extend it on both ways. Thus, BC is the graph of 3x + 2y = 4. Graph of 2x - 3y = 7 2x – 3y = 7 ? 3y = (2x – 7) ? y = ???? - ?? ?? …(ii) Putting x = 2, we get y = -1 Putting x = -1, we get y = -3 Putting x = 5, we get y = 1 Page 3 Exercise – 3A 1. Solve the system of equations graphically: 2x + 3y = 2, x – 2y = 8 Sol: On a graph paper, draw a horizontal line X'OX and a vertical line YOY' representing the x- axis and y-axis, respectively. Graph of 2x + 3y = 2 2x + 3y = 2 ?3y = (2 – 2x) ?3y = 2(1 – x) ?y = ?? (?? -?? ) ?? …(i) Putting x = 1, we get y = 0 Putting x = -2, we get y = 2 Putting x = 4, we get y = -2 Thus, we have the following table for the equation 2x + 3y = 2 x 1 -2 4 y 0 2 -2 Now, plot the points A(1, 0), B(-2, 2) and C(4, -2) on the graph paper. Join AB and AC to get the graph line BC. Extend it on both ways. Thus, the line BC is the graph of 2x + 3y = 2. Graph of x - 2y = 8 x – 2y = 8 ? 2y = (x – 8) ? y = ?? -?? ?? …(ii) Putting x = 2, we get y = -3 Putting x = 4, we get y = -2 Putting x = 0, we get y = -4 Thus, we have the following table for the equation x – 2y = 8. x 2 4 0 y -3 -2 - 4 Now, plot the points P(0, -4) and Q(2, -3). The point C(4, -2) has already been plotted. Join PQ and QC and extend it on both ways. Thus, line PC is the graph of x – 2y = 8. The two graph lines intersect at C(4, -2). ? x = 4 and y = -2 are the solutions of the given system of equations. 2. Solve the system of equations graphically: 3x + 2y = 4, 2x – 3y = 7 Sol: On a graph paper, draw a horizontal line X'OX and a vertical line YOY' representing the x- axis and y-axis, respectively. Graph of 3x + 2y = 4 3x + 2y = 4 ?2y = (4 – 3x) ?y = ?? - ???? ) ?? …(i) Putting x = 0, we get y = 2 Putting x = 2, we get y = -1 Putting x = -2, we get y = 5 Thus, we have the following table for the equation 3x + 2y = 4 x 0 2 -2 y 2 -1 5 Now, plot the points A(0, 2), B(2, -1) and C(-2, 5) on the graph paper. Join AB and AC to get the graph line BC. Extend it on both ways. Thus, BC is the graph of 3x + 2y = 4. Graph of 2x - 3y = 7 2x – 3y = 7 ? 3y = (2x – 7) ? y = ???? - ?? ?? …(ii) Putting x = 2, we get y = -1 Putting x = -1, we get y = -3 Putting x = 5, we get y = 1 Thus, we have the following table for the equation 2x – 3y = 7. x 2 -1 5 y -1 -3 1 Now, plot the points P(-1, -3) and Q(5, 1). The point C(2, -1) has already been plotted. Join PB and QB and extend it on both ways. Thus, line PQ is the graph of 2x – 3y = 7. The two graph lines intersect at B(2, -1). ?x = 2 and y = -1 are the solutions of the given system of equations. 3. Solve the system of equations graphically: 2x + 3y = 8, x – 2y + 3 = 0 Sol: On a graph paper, draw a horizontal line X'OX and a vertical line YOY' as the x-axis and y-axis, respectively. Graph of 2x + 3y = 8 2x + 3y = 8 ?3y = (8 – 2x) ?y = ?? - ???? ?? …(i) Putting x = 1, we get y = 2. Putting x = -5, we get y = 6. Putting x = 7, we get y = -2. Thus, we have the following table for the equation 2x + 3y = 8. x 1 -5 7 y 2 6 -2 Now, plot the points A(1, 2), B(5, -6) and C(7, -2) on the graph paper. Join AB and AC to get the graph line BC. Extend it on both ways. Thus, BC is the graph of 2x + 3y = 8. Page 4 Exercise – 3A 1. Solve the system of equations graphically: 2x + 3y = 2, x – 2y = 8 Sol: On a graph paper, draw a horizontal line X'OX and a vertical line YOY' representing the x- axis and y-axis, respectively. Graph of 2x + 3y = 2 2x + 3y = 2 ?3y = (2 – 2x) ?3y = 2(1 – x) ?y = ?? (?? -?? ) ?? …(i) Putting x = 1, we get y = 0 Putting x = -2, we get y = 2 Putting x = 4, we get y = -2 Thus, we have the following table for the equation 2x + 3y = 2 x 1 -2 4 y 0 2 -2 Now, plot the points A(1, 0), B(-2, 2) and C(4, -2) on the graph paper. Join AB and AC to get the graph line BC. Extend it on both ways. Thus, the line BC is the graph of 2x + 3y = 2. Graph of x - 2y = 8 x – 2y = 8 ? 2y = (x – 8) ? y = ?? -?? ?? …(ii) Putting x = 2, we get y = -3 Putting x = 4, we get y = -2 Putting x = 0, we get y = -4 Thus, we have the following table for the equation x – 2y = 8. x 2 4 0 y -3 -2 - 4 Now, plot the points P(0, -4) and Q(2, -3). The point C(4, -2) has already been plotted. Join PQ and QC and extend it on both ways. Thus, line PC is the graph of x – 2y = 8. The two graph lines intersect at C(4, -2). ? x = 4 and y = -2 are the solutions of the given system of equations. 2. Solve the system of equations graphically: 3x + 2y = 4, 2x – 3y = 7 Sol: On a graph paper, draw a horizontal line X'OX and a vertical line YOY' representing the x- axis and y-axis, respectively. Graph of 3x + 2y = 4 3x + 2y = 4 ?2y = (4 – 3x) ?y = ?? - ???? ) ?? …(i) Putting x = 0, we get y = 2 Putting x = 2, we get y = -1 Putting x = -2, we get y = 5 Thus, we have the following table for the equation 3x + 2y = 4 x 0 2 -2 y 2 -1 5 Now, plot the points A(0, 2), B(2, -1) and C(-2, 5) on the graph paper. Join AB and AC to get the graph line BC. Extend it on both ways. Thus, BC is the graph of 3x + 2y = 4. Graph of 2x - 3y = 7 2x – 3y = 7 ? 3y = (2x – 7) ? y = ???? - ?? ?? …(ii) Putting x = 2, we get y = -1 Putting x = -1, we get y = -3 Putting x = 5, we get y = 1 Thus, we have the following table for the equation 2x – 3y = 7. x 2 -1 5 y -1 -3 1 Now, plot the points P(-1, -3) and Q(5, 1). The point C(2, -1) has already been plotted. Join PB and QB and extend it on both ways. Thus, line PQ is the graph of 2x – 3y = 7. The two graph lines intersect at B(2, -1). ?x = 2 and y = -1 are the solutions of the given system of equations. 3. Solve the system of equations graphically: 2x + 3y = 8, x – 2y + 3 = 0 Sol: On a graph paper, draw a horizontal line X'OX and a vertical line YOY' as the x-axis and y-axis, respectively. Graph of 2x + 3y = 8 2x + 3y = 8 ?3y = (8 – 2x) ?y = ?? - ???? ?? …(i) Putting x = 1, we get y = 2. Putting x = -5, we get y = 6. Putting x = 7, we get y = -2. Thus, we have the following table for the equation 2x + 3y = 8. x 1 -5 7 y 2 6 -2 Now, plot the points A(1, 2), B(5, -6) and C(7, -2) on the graph paper. Join AB and AC to get the graph line BC. Extend it on both ways. Thus, BC is the graph of 2x + 3y = 8. Graph of x - 2y + 3 = 0 x – 2y + 3 = 0 ? 2y = (x + 3) ? y = ?? + ?? ?? …(ii) Putting x = 1, we get y = 2. Putting x = 3, we get y = 3. Putting x = -3, we get y = 0. Thus, we have the following table for the equation x – 2y + 3 = 0. x 1 3 -3 y 2 3 0 Now, plot the points P (3, 3) and Q (-3, 0). The point A (1, 2) has already been plotted. Join AP and QA and extend it on both ways. Thus, PQ is the graph of x – 2y + 3 = 0. The two graph lines intersect at A (1, 2). ? x = 1 and y = 2. 4. Solve the system of equations graphically: 2x - 5y + 4 = 0, 2x + y - 8 = 0 Sol: On a graph paper, draw a horizontal line X'OX and a vertical line YOY' as the x-axis and y-axis, respectively. Graph of 2x - 5y + 4 = 0 2x – 5y + 4 = 0 ?5y = (2x + 4) ?y = ???? + ?? ?? …(i) Page 5 Exercise – 3A 1. Solve the system of equations graphically: 2x + 3y = 2, x – 2y = 8 Sol: On a graph paper, draw a horizontal line X'OX and a vertical line YOY' representing the x- axis and y-axis, respectively. Graph of 2x + 3y = 2 2x + 3y = 2 ?3y = (2 – 2x) ?3y = 2(1 – x) ?y = ?? (?? -?? ) ?? …(i) Putting x = 1, we get y = 0 Putting x = -2, we get y = 2 Putting x = 4, we get y = -2 Thus, we have the following table for the equation 2x + 3y = 2 x 1 -2 4 y 0 2 -2 Now, plot the points A(1, 0), B(-2, 2) and C(4, -2) on the graph paper. Join AB and AC to get the graph line BC. Extend it on both ways. Thus, the line BC is the graph of 2x + 3y = 2. Graph of x - 2y = 8 x – 2y = 8 ? 2y = (x – 8) ? y = ?? -?? ?? …(ii) Putting x = 2, we get y = -3 Putting x = 4, we get y = -2 Putting x = 0, we get y = -4 Thus, we have the following table for the equation x – 2y = 8. x 2 4 0 y -3 -2 - 4 Now, plot the points P(0, -4) and Q(2, -3). The point C(4, -2) has already been plotted. Join PQ and QC and extend it on both ways. Thus, line PC is the graph of x – 2y = 8. The two graph lines intersect at C(4, -2). ? x = 4 and y = -2 are the solutions of the given system of equations. 2. Solve the system of equations graphically: 3x + 2y = 4, 2x – 3y = 7 Sol: On a graph paper, draw a horizontal line X'OX and a vertical line YOY' representing the x- axis and y-axis, respectively. Graph of 3x + 2y = 4 3x + 2y = 4 ?2y = (4 – 3x) ?y = ?? - ???? ) ?? …(i) Putting x = 0, we get y = 2 Putting x = 2, we get y = -1 Putting x = -2, we get y = 5 Thus, we have the following table for the equation 3x + 2y = 4 x 0 2 -2 y 2 -1 5 Now, plot the points A(0, 2), B(2, -1) and C(-2, 5) on the graph paper. Join AB and AC to get the graph line BC. Extend it on both ways. Thus, BC is the graph of 3x + 2y = 4. Graph of 2x - 3y = 7 2x – 3y = 7 ? 3y = (2x – 7) ? y = ???? - ?? ?? …(ii) Putting x = 2, we get y = -1 Putting x = -1, we get y = -3 Putting x = 5, we get y = 1 Thus, we have the following table for the equation 2x – 3y = 7. x 2 -1 5 y -1 -3 1 Now, plot the points P(-1, -3) and Q(5, 1). The point C(2, -1) has already been plotted. Join PB and QB and extend it on both ways. Thus, line PQ is the graph of 2x – 3y = 7. The two graph lines intersect at B(2, -1). ?x = 2 and y = -1 are the solutions of the given system of equations. 3. Solve the system of equations graphically: 2x + 3y = 8, x – 2y + 3 = 0 Sol: On a graph paper, draw a horizontal line X'OX and a vertical line YOY' as the x-axis and y-axis, respectively. Graph of 2x + 3y = 8 2x + 3y = 8 ?3y = (8 – 2x) ?y = ?? - ???? ?? …(i) Putting x = 1, we get y = 2. Putting x = -5, we get y = 6. Putting x = 7, we get y = -2. Thus, we have the following table for the equation 2x + 3y = 8. x 1 -5 7 y 2 6 -2 Now, plot the points A(1, 2), B(5, -6) and C(7, -2) on the graph paper. Join AB and AC to get the graph line BC. Extend it on both ways. Thus, BC is the graph of 2x + 3y = 8. Graph of x - 2y + 3 = 0 x – 2y + 3 = 0 ? 2y = (x + 3) ? y = ?? + ?? ?? …(ii) Putting x = 1, we get y = 2. Putting x = 3, we get y = 3. Putting x = -3, we get y = 0. Thus, we have the following table for the equation x – 2y + 3 = 0. x 1 3 -3 y 2 3 0 Now, plot the points P (3, 3) and Q (-3, 0). The point A (1, 2) has already been plotted. Join AP and QA and extend it on both ways. Thus, PQ is the graph of x – 2y + 3 = 0. The two graph lines intersect at A (1, 2). ? x = 1 and y = 2. 4. Solve the system of equations graphically: 2x - 5y + 4 = 0, 2x + y - 8 = 0 Sol: On a graph paper, draw a horizontal line X'OX and a vertical line YOY' as the x-axis and y-axis, respectively. Graph of 2x - 5y + 4 = 0 2x – 5y + 4 = 0 ?5y = (2x + 4) ?y = ???? + ?? ?? …(i) Putting x = -2, we get y = 0. Putting x = 3, we get y = 2. Putting x = 8, we get y = 4. Thus, we have the following table for the equation 2x - 5y + 4 = 0. x -2 3 8 y 0 2 4 Now, plot the points A (-2, 0), B (3, 2) and C(8, 4) on the graph paper. Join AB and BC to get the graph line AC. Extend it on both ways. Thus, AC is the graph of 2x - 5y + 4 = 0. Graph of 2x + y - 8 = 0 2x + y - 8 = 0 ? y = (8 – 2x) …(ii) Putting x = 1, we get y = 6. Putting x = 3, we get y = 2. Putting x = 2, we get y = 4. Thus, we have the following table for the equation 2x + y - 8 = 0. x 1 3 2 y 6 2 4 Now, plot the points P (1, 6) and Q (2, 4). The point B (3, 2) has already been plotted. Join PQ and QB and extend it on both ways. Thus, PB is the graph of 2x + y - 8 = 0. The two graph lines intersect at B (3, 2). ?x = 3 and y = 2 5. Solve the system of equations graphically: 3x + 2y = 12, 5x – 2y = 4 Sol: The given equations are: 3x + 2y = 12 …..(i)Read More

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- RS Aggarwal Solutions: Exercise 3B - Linear Equations in two variables
- RS Aggarwal Solutions: Exercise 3C - Linear Equations in two variables
- RS Aggarwal Solutions: Exercise 3D - Linear Equations in two variables
- RS Aggarwal Solutions: Exercise 3E - Linear Equations in two variables
- RS Aggarwal Solutions: Exercise 3F - Linear Equations in two variables