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Q7.    Draw the graphs of the equations x - y + 1=0 and 3x +2 y - 12=0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

Given, two equations, And  The points (x,y) satisfying (1) are  X 0 3 6 Y 1 4 7 And The points(x,y) satisfying (2) are, X 0 2 4 Y 6 3 0   GRAPH: 24151 As we can see from the graph that both lines intersect at the point (2,3), And the vertices of the Triangle are ( -1,0), (2,3) and (4,0). The area of the triangle is shaded with green colour. 

Q6.    Given the linear equation 2x + 3y -8 =0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:

            (iii) coincident lines

Given the equation, As we know that the condition for the coincidence  of the lines  , is, So any line with this condition can be   Here, As     the line satisfies the given condition.

Q6.    Given the linear equation 2x + 3y -8 =0, write another linear equation in two variables such that the geometrical representation of the pair so formed is

                (ii) parallel lines

Given the equation, As we know that the condition for the   lines  , for being parallel is, So Any line with this condition can be   Here, As     the line satisfies the given condition.

Q6.    Given the linear equation 2x + 3y -8 =0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
                (i) intersecting lines

Given the equation, As we know that the condition for the intersection of lines  , is , So Any line with this condition can be   Here, As     the line satisfies the given condition.

Q5.    Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

Let  be the length of the rectangular garden and  be the width. Now, According to the question, the length is 4 m more than its width.i.e. Also Given Half  Parameter of the rectangle = 36 i.e. Now, as we have two equations, on adding both equations, we get, Putting this in equation (1), Hence Length and width of the rectangle are 20m and 16 respectively.

Q4.    Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

                    (iv)    2x - 2y - 2 =0, \qquad 4x - 4y -5 = 0

Given, Equations, Comparing these equations with  , we get  As we can see  It means the given equations have no solution and thus pair of linear equations is inconsistent.

Q4.    Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

                (iii)    2x + y - 6 =0, \qquad 4x - 2 y - 4 = 0

Given, Equations, Comparing these equations with  , we get  As we can see  It means the given equations have exactly one solution and thus pair of linear equations is consistent. Now The points(x, y) satisfying the equation are, X 0 2 3 Y 6 2 0   And The points(x,y) satisfying the equation  are, X 0 1 2 Y -2 0 2   GRAPH: As we can see both lines intersects at point (2,2) and...

Q4.    Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

                (ii)    x - y = 8,\qquad 3x - 3y = 16

Given, Equations, Comparing these equations with  , we get  As we can see  It means the given equations have no solution and thus pair of linear equations is inconsistent.

Q4.    Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

                    (i)    x + y = 5 \qquad 2x + 2 y = 10

Given, Equations, Comparing these equations with  , we get  As we can see  It means the given equations have an infinite number of solutions and thus pair of linear equations is consistent. The points (x,y) which satisfies in both equations are  X 1 3 5 Y 4 2 0 .

Q3.    On comparing the ratios \frac{a_1}{a_2}\frac{b_1}{b_2} and \frac{c_1}{c_2},  find out whether the following pair of linear equations are consistent, or inconsistent

                (v)    \frac{4}{3}x + 2y = 8; \qquad 2x + 3y = 12

Given, Equations, Comparing these equations with  , we get  As we can see  It means the given equations have an infinite number of solutions and thus pair of linear equations is consistent.

Q3.    On comparing the ratios \frac{a_1}{a_2}\frac{b_1}{b_2} and \frac{c_1}{c_2}, find out whether the lines representing the following pairs of linear equations are consistent, or inconsistent:

                    (iv)    5x - 3y = 11;\qquad -10x + 6y =-22

Given, Equations, Comparing these equations with  , we get  As we can see  It means the given equations have an infinite number of solutions and thus pair of linear equations is consistent.

Q3.    On comparing the ratios \frac{a_1}{a_2}\frac{b_1}{b_2} and \frac{c_1}{c_2}, find out whether the lines representing the following pairs of linear equations are consistent, or inconsistent:

                    (iii)    \frac{3}{2}x + \frac{5}{3}y = 7;\qquad 9x -10y = 14

Given, Equations, Comparing these equations with  , we get  As we can see  It means the given equations have exactly one solution and thus pair of linear equations is consistent.

Q3.    On comparing the ratios \frac{a_1}{a_2}\frac{b_1}{b_2} and \frac{c_1}{c_2}, find out whether the lines representing the following pairs of linear equations are consistent, or inconsistent:

                    (ii)    2x - 3y = 8;\qquad 4x - 6y = 9

Given, Equations, Comparing these equations with  , we get  As we can see  It means the given equations have no solution and thus pair of linear equations is inconsistent.

Q2.    On comparing the ratios \frac{a_1}{a_2}\frac{b_1}{b_2} and \frac{c_1}{c_2}, find out whether the lines representing the following pairs of linear equations are consistent, or inconsistent:

                    (i)    3x + 2y = 5;\qquad 2x - 3y = 7

Give, Equations, Comparing these equations with  , we get  As we can see  It means the given equations have exactly one solution and thus pair of linear equations is consistent.

Q2.    On comparing the ratios \frac{a_1}{a_2}\frac{b_1}{b_2} and \frac{c_1}{c_2}, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:

                    (iii)    \\6x - 3y + 10 = 0\\ 2x - y+ 9 = 0

Give, Equations, Comparing these equations with  , we get  As we can see  It means that both lines are parallel to each other.

Q2.    On comparing the ratios \frac{a_1}{a_2}\frac{b_1}{b_2} and \frac{c_1}{c_2}, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:

                    (ii)    \\9x + 3y + 12 = 0\\ 18x + 6y + 24 = 0

Given, Equations, Comparing these equations with  , we get  As we can see  It means that both lines are coincident.

Q2.    On comparing the ratios \frac{a_1}{a_2}\frac{b_1}{b_2} and \frac{c_1}{c_2}, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:

                    (i)    \\5x - 4y + 8 = 0\\ 7x + 6y - 9 = 0

Give, Equations, Comparing these equations with  , we get  As we can see  It means that both lines intersect at exactly one point.

Q1.    Form the pair of linear equations in the following problems, and find their solutions graphically.

                    (ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.

Let x be the price of 1 pencil and y be the price of 1 pen, Now, According to the question And  Now, The points (x,y), that satisfies the equation (1) are  X 3 -4 10 Y 5 10 0 And, The points(x,y) that satisfies the equation (2) are  X 3 8 -2 Y 5 -2 12 The Graph, As we can see from the Graph, both line intersects at point (3,5) that is, x = 3 and y = 5 which means cost of 1...

Q1.    Form the pair of linear equations in the following problems, and find their solutions graphically.

                (i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

Let the number of boys be x and the number of girls be y.  Now, According to the question, Total number of students in the class = 10, i.e. And the number of girls is 4 more than the number of boys,i.e. Different points (x, y) for equation (1) X 5 6 4 Y 5 4 6 Different points (x,y) satisfying (2) X 5 6 7 y 1 2 3   Graph, As we can see from the graph, both lines intersect at...
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