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

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(a)

(b)

(c)

(a)

(b)

(c)

## (3) Answer the Following Question

(a) , express βmβ in terms of βnβ .

(b) , express βxβ in terms of βyβ .

## (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.

## Help Krishna to Find Out this Two Number

• Here in the given equation, there are two variable.
• One is βxβ and another one in βyβ .
• So, this equation has two variables.
• So ,

• Here in the given equation, there are two variables.
• One is βaβ and another one in βbβ .
• So, this equation has two variables.
• So ,

• Given equation has only one variable βxβ , βx2β is a square of variable βxβ .
• So, this equation has only one variable.

• Given equation has only one variable βbβ .
• So, this equation has only one variable.

• Given equation has only one variable βcβ .
• So, this equation has only one variable.

• Here in the given equation, there are two variables.
• One is βmβ and another one in βnβ .
• So, this equation has two variables.
• So ,

• Now to express βmβ in terms of βnβ
• (Take term from left side to right side)
• Now divide by 4 on both side,

• Add 16 on both side,

• Now subtract β8yβ from both sides.

• 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yβ

• 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.

• 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.

• Suppose this two number is βaβ and βbβ .
• And βaβ is larger number than βbβ
• βbβ is smaller number than βaβ .
• 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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