# NCERT Class 10 Mathematics Linear Equation Formative Assessment CBSE Board Sample Problems Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Linear Equation Formative Assessment

Question 1. Which of these equation have i) Unique solution ii) Infinite solutions iii) no solutions

a)

b)

c)

d)

e)

f)

g)

h)

Solution

 Condition Algebraic interpretation One unique solution only Infinite solution No solution

One unique solution: (a) , (d) , (e) , (f) , (d)

Infinite solution: (b)

No solution: (e) , (h)

Question 2. Using substitution method solve the below equation

a)

b)

Solution

 1 Method of elimination by substitution 1) Suppose the equation are2) Find the value of variable of either x or y in other variable term in first equation3) Substitute the value of that variable in second equation4) Now this is a linear equation in one variable. Find the value of the variable5) Substitute this value in first equation and get the second variable

a) From 1st equation

Substituting this in second equation

Putting this 1st equation

b) (1,0)

Question 3. Using elimination method, solve the following

a)

b)

Solution

 1 Method of elimination by equating the coefficients 1) Suppose the equation are2) Find the LCM of and . Let it k.3) Multiple the first equation by the value 4) Multiple the first equation by the value 4) Subtract the equation obtained. This way one variable will be eliminated and we can solve to get the value of variable y5) Substitute this value in first equation and get the second variable

a) … (1)

… (2)

Multiplying equation (1) by 7

… (3)

Subtracting equation 2 from equation 7

We get

Substituting this in (1) , we get x = 15

b) (8,6)

Question 4. Solve the below linear equation using cross-multiplication method

a)

b)

Solution

 3 Cross Multiplication method 1) Suppose the equation are2) This can be written as3) This can be written as4) Value of x and y can be find using the first and last expression second and last expression

a) The equation can be written as

By cross multiplication we have

Solving

b)