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If the equation 2x+3y+1=0,3x+y-2=0, and ...

If the equation `2x+3y+1=0,3x+y-2=0, and a x+2y-b=0` are consistent, then prove that `a-b=2.`

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To prove that \( a - b = 2 \) given the equations \( 2x + 3y + 1 = 0 \), \( 3x + y - 2 = 0 \), and \( ax + 2y - b = 0 \) are consistent, we can follow these steps: ### Step 1: Write the equations in standard form We have the following equations: 1. \( 2x + 3y + 1 = 0 \) (Equation 1) 2. \( 3x + y - 2 = 0 \) (Equation 2) 3. \( ax + 2y - b = 0 \) (Equation 3) ...
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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. Let {D1, D2, D3 ,Dn} be the set of third order determinant that can be...

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  2. If g(x)-(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of d...

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  3. If the equation 2x+3y+1=0,3x+y-2=0, and a x+2y-b=0 are consistent, t...

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  4. If w is a complex cube root of unity, then value of =|[a1+b1w, a1w^2+b...

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  5. Let f(x)=|[cos(x+x^2),sin(x+x^2),-cos(x+x^2)],[sin(x-x^2),cos(x-x^2), ...

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  6. Which of the following has/have value equal to zero? |8 2 7 12 3 5 16 ...

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  7. If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove t...

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  8. If a ,b ,c are in G.P. with common ratio r1a n dalpha,beta,gamma are...

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  9. Show that: |a, b-c,c+b, a+c, b, c-a,a-b,b+a, c|=(a+b+c)(a^2+b^2+c^2)d...

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  10. In triangle A B C , if |1, 1, ,1,cotA/2,cotB/2,cotC/2,tanB/2+tanC/2,ta...

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  11. If a ,b ,c ,d ,e, and fare in G.P. then the value of |((a^2),(d^2),x)...

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  12. Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a...

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  13. If xi=ai bi c+i,i=1,,23 are three-digit positive integer such that ...

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  14. The system of linear equations x+lambday-z=0, lambdax-y-z=0, x+y-lam...

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  15. If a , b ,c are all different and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^...

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  16. If p q r!=0 and the system of equation (p+a)x+b y+c z=0, a x+(q+b)y+c...

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  17. If c<1 and the system of equations x+y-1=0,2x-y-c=0,a n d -b x+3b y-c=...

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  18. Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(x-...

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  19. If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c]...

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  20. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

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