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Show that each of the following system...

Show that each of the following systems of linear equations is consistent and also find their solutions: `6x+4y=2` `9x+6y=3`

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To determine if the system of linear equations is consistent and to find their solutions, we will analyze the given equations step by step. ### Given Equations: 1. \( 6x + 4y = 2 \) (Equation 1) 2. \( 9x + 6y = 3 \) (Equation 2) ### Step 1: Check for Consistency To check if the system is consistent, we can determine if the two equations represent the same line or different lines. We can do this by manipulating the equations. ...
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RD SHARMA-SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS-Solved Examples And Exercises
  1. Solve the following system of equations by matrix method : 2...

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  2. Show that each of the following systems of linear equations is consi...

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  3. Solve the following system of equations by matrix method : 5x+7y+2...

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  4. If A=((2,-3,5),(3,2,-4),(1,1,-2)) find A^(-1). Use it to solve the sys...

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  5. For the system of equitions: x+2y+3z=1 2x+y+3z=2 5x+5y+9z=4 there i...

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  6. Let a ,b , c be the real numbers. The following system of equations in...

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  7. The existence of the unique solution of the system of equations: x+y+z...

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  8. Let x=[x1x2x3],A=[1-1 2 2 0 1 3 2 1]a n dB=[3 2 1]dotIfA X=B , Then X ...

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  9. The system of equations: x+y+z=5 x+2y+3z=9 x+3y+lambdaz=mu has a un...

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  10. The number of solution of the system of equations: 2x+y-z=7 x-3y+2z=1...

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  11. The system of equation x+y+z=2,3x-y+2z=6a n d3x+y+z=-18 has a unique s...

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  12. Solve the following system of homogeneous equations: 2x+3y-z=0 x-y-2z...

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  13. Given A=[[1,-1, 0], [2, 3, 4], [0, 1, 2]], B= [[2,2,-4],[-4,2,-4],[2,-...

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  14. If a1x+b1y+c1z=0, a2x+b2y+c2z=0, a3x+b3y+c3z=0 and |(a1,b1,c1),(a2,b...

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  15. Solve the following system of homogeneous equations: x+y-z=0 x-2y+...

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  16. If A=[[1,-1, 1],[ 2, 1,-3],[ 1, 1, 1]], find A^(-1) and hence solve th...

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  17. Show that the following system of equation is consistent. 2x-y+3z=5,3x...

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  18. Solve the following system of equations, using matrix method. x+2y+z=7...

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  19. The number of solutions of the system of equations: 2x+y-z=7 x-3y+2z=...

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  20. An amount of Rs 5000 is put into three investments at the rate of inte...

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