Grade 8 Simultaneous Linear Equation Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) in Each Equation, Put a Tick (√) if It is a Two-Variable Linear Equation and a Cross (Γ—) if It is Not

(a)

(b)

(c)

(2) in Each Equation, Put a Tick (√) if It is a Two-Variable Linear Equation and a Cross (X) if It is Not

(a)

(b)

(c)

(3) Answer the Following Question

(a) , express β€œm” in terms of β€œn” .

(b) , express β€œx” in terms of β€œy” .

(4) Solve the Given Simultaneous Linear Equations Using the Substitution Method

(a) Solve , and verify the solution.

(5) Solve the Given Simultaneous Linear Equations Using the Elimination Method

(a) Solve and verify the solution.

(6) Krishna՚s Friend Mehul Challenged Her to a Number Game. Mehul Thought of Two Numbers and Asked Krishna to Find Them. He Said That the Number is in Such a Way That β€œFour Times the Smaller Exceeds Two Times Larger by Four and Six Times Smaller Exceeds Four Times Larger by Four”

Help Krishna to Find Out this Two Number

Answers and Explanations

Answer 1 (A)

  • Here in the given equation, there are two variable.
  • One is β€œx” and another one in β€œy” .
  • So, this equation has two variables.
  • So ,

Answer 1 (B)

  • Here in the given equation, there are two variables.
  • One is β€œa” and another one in β€œb” .
  • So, this equation has two variables.
  • So ,

Answer 1 (C)

  • Given equation has only one variable β€œx” , β€œx2” is a square of variable β€œx” .
  • So, this equation has only one variable.

Answer 2 (A)

  • Given equation has only one variable β€œb” .
  • So, this equation has only one variable.

Answer 2 (B)

  • Given equation has only one variable β€œc” .
  • So, this equation has only one variable.

Answer 2 (C)

  • Here in the given equation, there are two variables.
  • One is β€œm” and another one in β€œn” .
  • So, this equation has two variables.
  • So ,

Answer 3 (A)

  • Now to express β€œm” in terms of β€œn”
  • (Take term from left side to right side)
  • Now divide by 4 on both side,

Answer 3 (B)

  • Add 16 on both side,

  • Now subtract β€œ8y” from both sides.

Answer 4 (A)

  • From above two equations, first take any of one equation and solve any of the one variable than plug its value in to another equation to get answer.
  • We have two equation,

  • Now solve second equation for β€œy”

  • Now plug in to the value of y in to the first equation,
  • So ,

  • Now plug the value of x in to y to get value of y ,

  • So ,
  • Now to verify the value of x and y , put this value in ay of given equation,
  • So,

  • So, value verified.

Answer 5 (A)

  • Multiply each equation by suitable number so that two equations have the same leading coefficient.
  • For that multiply first equation by one and second by 2.
  • So, we get

  • Hence,

  • Now substitute second equation from first equation
  • So,

  • Now put the value of y in first equation to get the value of x.

  • So ,
  • Now to verify solution put the value of x and y in any equation
  • We put value of x and y in first equation.
  • So,

  • Hence verified.

Answer (6)

  • Suppose this two number is β€œa” and β€œb” .
  • And β€œa” is larger number than β€œb”
  • β€œb” is smaller number than β€œa” .
  • Now four times the smaller exceeds two times larger by three,
  • So our equation is,

  • And six times smaller exceeds four times larger by four
  • So our equation is,

  • Now we have two equation,

  • Now to solve this we have multiplied equation-1 by 2 and then substitute it from equation (2) .

  • Now we put in equation (1) to get another number.

  • Therefore, both number are 2.

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