Home
Class 10
MATHS
Are the following pair of linear equatio...

Are the following pair of linear equations consistent ? Justify your answer.
(i) `-3x - 4y = 12` and ` 4y + 3x = 12`
(ii) `(3)/(5)x - y = (1)/(2)` and `(1)/(5) x - 3y = (1)/(6) `
(iii) `2ax + by = a` and `4ax + 2by - 2a = 0, a, b != 0`
(iv) `x + 3y = 11` and `2(2x + 6y) = 22`

Text Solution

AI Generated Solution

To determine whether the given pairs of linear equations are consistent, we will use the condition for consistency. A pair of linear equations is consistent if the ratio of the coefficients of x and y is not equal to the ratio of the constants. ### Step-by-Step Solution: **(i)** For the equations: 1. \(-3x - 4y = 12\) 2. \(4y + 3x = 12\) ...
Promotional Banner

Topper's Solved these Questions

  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    NCERT EXEMPLAR ENGLISH|Exercise Exercise 3.3 Short Answer Type Questions|22 Videos

  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    NCERT EXEMPLAR ENGLISH|Exercise Exercise 3.4 Long Answer Type Questions|13 Videos

  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    NCERT EXEMPLAR ENGLISH|Exercise Exercise 3.4 Long Answer Type Questions|13 Videos

  • INTRODUCTION TO TRIGoNOMETRY AND ITS APPLICATIONS

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPES QUESTIONS|18 Videos

  • POLYNOMIALS

    NCERT EXEMPLAR ENGLISH|Exercise Long Answer Type Questions|6 Videos

Similar Questions

Explore conceptually related problems

Do the following pair of linear equations have no solution ? Justify your answer. (i) 2x + 4y = 3 and 12y +6x = 6 (ii) x = 2y and y = 2x (iii) 3x + y - 3 = 0 and 2x + (2)/(3)y = 2

Solve the following pair of linear equatio: 3x-5y-4=0 9x=2y+7

Do the following equations represent a pair of coincident lines ? Justify your answer. (i) 3x + (1)/(7)y = 3 and 7x + 3y = 7 (ii) -2x - 3y = 1 and 6y + 4x = -2 (iii) (x)/(2) + y + (2)/(5) = 0 and 4x + 8y + (5)/(16) = 0

Reduce the following equations into intercept form and find their intercepts on the axes.(i) 3x + 2y 12 = 0 , (ii) 4x 3y = 6 , (iii) 3y + 2 = 0 .

Solve the following paris of linear (simultaneous) equation using method of elimination by substution: (2x + 1)/(7) + (5y - 3)/(3) = 12 (3x + 2)/(2) - (4y - 3)/(9) = 13

Reduce the following equations into intercept form and find their intercepts on the axes.(i) 3x + 2y -12 = 0 , (ii) 4x - 3y = 6 , (iii) 3y + 2 = 0 .

Draw the graph of each of the following linear equations in two variables: (i) x+y=4 (ii) x-y=2 (iii) y=3x (iv) 3=2x+y

Solve the following pair of linear (simultaneous) equation using method of substitution. {:((2x+1)/(7)+(5y-3)/(3)=12),((3x+2)/(2)-(4y+3)/(9)=13)):}

Draw the graph of each of the following linear equations in two variables:(i) x+y=4 (ii) x-y=2 (iii) y=3x (iv) 3=2x+y

The equation of the directrix of the parabola x^(2) - 4x - 8y + 12 = 0 is (i) y = 0 (ii) x - 1 = 0 (iii) y+ 1 = 0 (iv) x + 1 = 0