## RS Aggarwal Class 10 Solutions Chapter 3 Linear equations in two variables Test Yourself

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Test Yourself.

### RS Aggarwal Solutions Class 10 Chapter 3

- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3A
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3B
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3C
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3D
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3E
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3F
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables MCQS
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Test Yourself

**MCQ**

**Question 1.**

**The graphic representation of the equations x + 2y = 3 and 2x + 4y + 1 = 0 gives a pair of**

**(a) parallel lines**

**(b) intersecting lines**

**(c) coincident lines**

**(d) none of these**

**Solution:**

**(a)**

**Question 2.**

**If 2x – 3y = 7 and (a + b) x – (a + b -3) y = 4a + b have an infinite number of solutions then**

**(a) a = 5, b = 1**

**(b) a = -5, b = 1**

**(c) a = 5, b = -1**

**(d) a = -5, b = -1**

**Solution:**

**(d)**

**Question 3.**

**The pair of equations 2x + y = 5, 3x + 2y = 8 has**

**(a) a unique solution**

**(b) two solutions**

**(c) no solutions**

**(d) infinitely many solutions**

**Solution:**

**(a)**

**Question 4.**

**If x = -y and y > 0, which of the following is wrong?**

**(a) x²y > 0**

**(b) x + y = 0**

**(c) xy < 0**

**(d) – = 0**

**Solution:**

**(d)**

**Short-Answer Questions**

**Question 5.**

**Show that the system of equations -x + 2y + 2 = 0 and x – y – 1 = 0 has a unique solution.**

**Solution:**

**Question 6.**

**For what values of k is the system of equations kx + 3y = k – 2, 12x + ky = k inconsistent?**

**Solution:**

**Question 7.**

**Solution:**

**Question 8.**

**Solve the system of equations x – 2y = 0, 3x + 4y = 20.**

**Solution:**

**Question 9.**

**Show that the paths represented by the equations x – 3y = 2 and -2x + 6y = 5 are parallel.**

**Solution:**

**Question 10.**

**The difference between two numbers is 26 and one number is three times the other. Find the numbers.**

**Solution:**

Let first number = x

and second number = y

According to the conditions, x – y = 26 …(i)

and x = 3y …..(ii)

From (i),

3y – y = 26

⇒ 2y = 26

⇒ y = 13

and x = 3 x 13 = 39

Numbers are 39 and 13

**Short-Answer Questions (3 marks)**

**Question 11.**

**Solve : 23x + 29y = 98, 29x + 23y = 110.**

**Solution:**

23x + 29y = 98 …..(i)

29x + 23y = 110 …..(ii)

Adding, we get 52x + 52y = 208

x + y = 4 …..(iii) (Dividing by 52)

and subtracting,

-6x + 6y = -12

x – y = 2. …..(iv) (Dividing by -6)

Adding (iii) and (iv),

2x = 6 ⇒ x = 3

Subtracting,

2x = 2 ⇒ y = 1

Hence, x = 3, y = 1

**Question 12.**

**Solve : 6x + 3y = 7xy and 3x + 9y = 11xy.**

**Solution:**

x = 1, y =

**Question 13.**

**Find the value of k for which the system of equations 3x + y = 1 and kx + 2y = 5 has (i) a unique solution, (ii) no solution.**

**Solution:**

**Question 14.**

**In a ∆ABC, ∠C = 3∠B = 2 (∠A + ∠B). Find the measure of each one of ∠A, ∠B and ∠C.**

**Solution:**

**Question 15.**

**5 pencils and 7 pens together cost ₹ 195 while 7 pencils and 5 pens together cost ₹ 153. Find the cost of each one of the pencil and the pen.**

**Solution:**

Let cost of one pencil = ₹ x

and cost of one pen = ₹ y

According to the condition,

5x + 7y = 195 …(i)

7x + 5y= 153 …(ii)

Adding, (i) and (ii)

12x + 12y = 348

x + y = 29 ….(iii) (Dividing by 12)

and subtracting,

-2x + 2y = 42

-x + y = 21 …..(iv) (Dividing by -2)

Now, Adding (iii) and (iv),

2y = 50 ⇒ y = 25

and from (iv),

-x + 25 = 21 ⇒ -x = 21 – 25 = -4

x = 4

Cost of one pencil = ₹ 4

and cost of one pen = ₹ 25

**Question 16.**

**Solve the following system of equations graphically:**

**2x – 3y = 1, 4x – 3y + 1 = 0.**

**Solution:**

2x – 3y = 1, 4x – 3y + 1 = 0

2x – 3y = 1

2x = 1 + 3y

x =

Giving some different values to y, we get corresponding values of x as given below

Now plot the points (2, 1), (5, 3) and (-1, -1) on the graph and join them to get a line.

Similarly,

4x – 3y + 1 = 0

⇒ 4x = 3y – 1

⇒ x =

Now plot the points (-1, -1), (-4, -5) and (2, 3) on the graph and join them to get another line which intersects the first line at the point (-1, -1).

Hence, x = -1, y = -1

**Long-Answer Questions**

**Question 17.**

**Find the angles of a cyclic quadrilateral ABCD in which ∠A = (4x + 20)°, ∠B = (3x – 5)°, ∠C = (4y)° and ∠D = (7y + 5)°.**

**Solution:**

We know that opposite angles of a cyclic quadrilateral are supplementary.

∠A + ∠C = 180° and ∠B + ∠D = 180°

Now, ∠A = 4x° + 20°, ∠B = 3x° – 5°, ∠C = 4y° and ∠D = 7y° + 5°

But ∠A + ∠C = 180°

4x + 20° + 4y° = 180°

⇒ 4x + 4y = 180° – 20 = 160°

x + y = 40° …(i) (Dividing by 4)

and ∠B + ∠D = 180°

⇒ 3x – 5 + 7y + 5 = 180°

⇒ 3x + 7y = 180° …(ii)

From (i), x = 40° – y

Substituting the value of x in (ii),

3(40° – y) + 7y = 180°

⇒ 120° – 3y + 7y = 180°

⇒ 4y = 180°- 120° = 60°

y = 15°

and x = 40° – y = 40° – 15° = 25°

∠A = 4x + 20 = 4 x 25 + 20 = 100 + 20= 120°

∠B = 3x – 5 = 3 x 25 – 5 = 75 – 5 = 70°

∠C = 4y = 4 x 15 = 60°

∠D = 7y + 5 = 7 x 15 + 5 = 105 + 5 = 110°

**Question 18.**

**Solve for x and y :**

**Solution:**

**Question 19.**

**If 1 is added to both the numerator and the denominator of a fraction, it becomes . If, however, 5 is subtracted from both numerator and the denominator, the fraction becomes . Find the fraction.**

**Solution:**

Let numerator of a fraction = x

and denominator = y

Fraction =

According to the conditions,

**Question 20.**

**Solve : – = a + b, ax – by = 2ab.**

**Solution:**

Hope given RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Test Yourself are helpful to complete your math homework.

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