Find the equation of the straight line passing through the origin and through the point of intersection of the lines 5x + 7y = 3 and 2x - 3y = 7.

5x + 7y = 3 ....(i) 2x - 3y = 7 ....(ii) Multiply (i) by 3 and (ii) by 7, 15x + 21y = 9 ....(iii) 14x - 21y = 49 ....(iv) Adding (iii) and (iv) we get, ⇒ 29x = 58 ⇒ x = 2. Substituting x = 2 in (i), we get ⇒ 5(2) + 7y = 3 ⇒ 10 + 7y = 3 ⇒ 7y = 3 - 10 ⇒ 7y = -7 ⇒ y = -1. Hence, the point of intersection of lines is (2, -1). The equation of the line joining (2, -1) and (0, 0) will be given by two-point form i.e., Putting values in above equation we get, Hence, the equation of the line is x + 2y = 0.

Find the equations of the diagonals of a rectangle whose sides are x = -1, x = 2, y = -2 and y = 6.

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(i) Write down the coordinates of point P that divides the line joining A(-4, 1) and B(17, 10) in the ratio 1 : 2.
(ii) Calculate the distance OP, where O is the origin.
(iii) In what ratio does the y-axis divide the line AB?

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The line through P(5, 3) intersects y-axis at Q.
(i) Write the slope of the line.
(ii) Write the equation of the line.
(iii) Find the co-ordinates of Q.

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M and N are two points on the x-axis and y-axis respectively. P(3, 2) divides the line segment MN in the ratio 2 : 3. Find :
(i) the coordinates of M and N.
(ii) slope of the line MN.

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Mathematics

Find the equation of the straight line passing through the origin and through the point of intersection of the lines 5x + 7y = 3 and 2x - 3y = 7.

Straight Line Eq

Related Questions

Find the equations of the diagonals of a rectangle whose sides are x = -1, x = 2, y = -2 and y = 6.

(i) Write down the coordinates of point P that divides the line joining A(-4, 1) and B(17, 10) in the ratio 1 : 2.
(ii) Calculate the distance OP, where O is the origin.
(iii) In what ratio does the y-axis divide the line AB?

The line through P(5, 3) intersects y-axis at Q.
(i) Write the slope of the line.
(ii) Write the equation of the line.
(iii) Find the co-ordinates of Q.

M and N are two points on the x-axis and y-axis respectively. P(3, 2) divides the line segment MN in the ratio 2 : 3. Find :
(i) the coordinates of M and N.
(ii) slope of the line MN.

Mathematics

Find the equation of the straight line passing through the origin and through the point of intersection of the lines 5x + 7y = 3 and 2x - 3y = 7.

Straight Line Eq

Related Questions

Find the equations of the diagonals of a rectangle whose sides are x = -1, x = 2, y = -2 and y = 6.

(i) Write down the coordinates of point P that divides the line joining A(-4, 1) and B(17, 10) in the ratio 1 : 2.(ii) Calculate the distance OP, where O is the origin.(iii) In what ratio does the y-axis divide the line AB?

The line through P(5, 3) intersects y-axis at Q.(i) Write the slope of the line.(ii) Write the equation of the line.(iii) Find the co-ordinates of Q.

M and N are two points on the x-axis and y-axis respectively. P(3, 2) divides the line segment MN in the ratio 2 : 3. Find :(i) the coordinates of M and N.(ii) slope of the line MN.

(i) Write down the coordinates of point P that divides the line joining A(-4, 1) and B(17, 10) in the ratio 1 : 2.
(ii) Calculate the distance OP, where O is the origin.
(iii) In what ratio does the y-axis divide the line AB?

The line through P(5, 3) intersects y-axis at Q.
(i) Write the slope of the line.
(ii) Write the equation of the line.
(iii) Find the co-ordinates of Q.

M and N are two points on the x-axis and y-axis respectively. P(3, 2) divides the line segment MN in the ratio 2 : 3. Find :
(i) the coordinates of M and N.
(ii) slope of the line MN.