LINEAR EQUATIONS WORKSHEET WITH ANSWERS

Question 1 :

Solve for r : 

7r + 7 = 13 + 6r

Question 2 :

Solve for x : 

13 - 4x = 1 - x

Question 3 :

Solve for x. 

-7x - 3x + 2 = -8x - 8

Question 4 :

Solve for b : 

-14 + 6b + 7 - 2b = 1 + 5b

Question 5 :

Solve for x : 

-6x - 20 = -2x + 4(1 - 3x)

Question 6 :

Solve for n : 

4n - 40 = 7(-2n + 2)

Question 7 :

Solve for x : 

-31 - 4x = -5 - 5(1 + 5x)

Question 8 :

Solve for x 

-3(x - 1) + 8(x - 3) = 6x + 7 - 5x

Question 9 :

Solve for x : 

4(-8x + 5)  =  -32x - 26

Question 10 : 

Solve the following equation : 

(1/2)(8y - 6)  =  5y - (y + 3)

Question 11 :

Solve the following system of linear equations using elimination method.

3x + 2y = 8

7x - 2y = 12

Question 12 :

Solve the following system of linear equations substitution method.

y = 7x - 3

x + 3y = 13

Question 13 :

The denominator of a fraction exceeds the numerator by 5. If 3 be added to both, the fraction becomes 3/4. Find the fraction.

Question 14 :

The total number of students in a school is 501. If the number of boys is equal to 3 more than twice the number of girls, find the number of boys and girls. 

Answers

1. Answer :

7r + 7 = 13 + 6r

Subtract 6r from each side.

r + 7 = 13

Subtract 7 from each side. 

r = 6

2. Answer :

13 - 4x = 1 - x

Add 4x to each side.

13 = 1 + 3x

Subtract 1 from each side. 

12 = 3x

Divide each side by 3. 

4 = x

3. Answer :

-7x - 3x + 2 = -8x - 8

Combine the like terms. 

-10x + 2 = -8x - 8

Add 10x to each side. 

2 = 2x - 8

Add 8 to each side.

10 = 2x

Divide each side by 2. 

5 = x

4. Answer :

-14 + 6b + 7 - 2b = 1 + 5b

Combine the like terms. 

4b - 7 = 1 + 5b

Subtract 4b from each side. 

-7 = 1 + b 

Subtract 1 from each side.

-8 = b

5. Answer :

-6x - 20 = -2x + 4(1 - 3x)

Simplify. 

-6x - 20 = -2x + 4 - 12x

-6x - 20 = 4 - 14x

Add 14x to each side. 

8x - 20 = 4

Add 20 to each side.

8x = 24

Divide each side by 8.

x = 3

6. Answer :

4n - 40 = 7(-2n + 2)

Simplify.

4n - 40 = -14n + 14

Add 14n to each side. 

18n - 40 = 14

Add 40 to each side. 

18n = 54

Divide each side by 18. 

n = 3

7. Answer :

-31 - 4x = -5 - 5(1 + 5x)

Simplify. 

-31 - 4x = -5 - 5 - 25x

-31 - 4x = -10 - 25x

Add 21x to each side. 

-31 + 21x = -10

Add 31 to each side. 

21x = 21

Divide each side by 21. 

x = 1

8. Answer :

-3(x - 1) + 8(x - 3) = 6x + 7 - 5x

Simplify. 

-3x + 3 + 8x - 24 = x + 7

5x - 21 = x + 7

Subtract x from each side. 

4x - 21 = 7

Add 21 to each side. 

4x = 28

Divide each side by 4.

x = 7

9. Answer :

4(-8x + 5) = -32x - 26

Simplify.

-32x + 20 = -32x - 26

Add 32x to each side. 

20 = -26

In the final step of solving the given equation, the variable 'x' is no more.

And also, the result '20 = -26' is false. 

So, the given equation has no solution.

10. Answer :

(1/2)(8y - 6) = 5y - (y + 3)

Simplify both sides. 

4y - 3 = 5y - y - 3

4y - 3 = 4y - 3  

Subtract 4y from each side. 

-3 = -3

In the final step of solving the given equation, the variable 'x' is no more.

And also, the result '-3 = -3' is true. 

Because the result is true, the given equation is true for all real values of x. 

So, the given equation has infinitely has many solutions.

11. Answer :

3x + 2y = 8 ----(1)

7x - 2y = 12 ----(2)

In the above two equations, the coefficient of y-terms are same with different signs.

By adding those two equations, you can eliminate y-terms.

(1) + (2) :

10x = 20

Divide both sides by 10.

x = 2

Substitute x = 2 in (1).

3(2) + 2y = 8

6 + 2y = 8

Subtract 6 from both sides.

2y = 2

Divide both sides by 2.

y = 1

Therefore, the solutions for the given system of linear equations are

x = 2 and y = 1

12. Answer :

y = 7x - 3 ----(1)

x + 3y = 13 ----(2)

Substitute y = 7x - 3 in (1).

x + 3(7x - 3) = 13

Use Distributive Property.

x + 21x - 9 = 13

22x - 9 = 13

Add 9 to both sides.

22x = 22

Divide both sides by 22.

x = 1

Substitute x = 1 in (1).

y = 7(1) - 3

y = 7 - 3

y = 4

Therefore, the solutions for the given system of linear equations are

x = 1 and y = 4

13. Answer :

Let x be the numerator.

Since the denominator of the fraction exceeds the numerator by 5, the fraction is 

= x/(x + 5) ----(1)

Given : If 3 be added to both, the fraction becomes 3/4.

From the above information, we have

(x + 3)/(x + 5 + 3) = 3/4

Simplify.

(x + 3)/(x + 8) = 3/4

4(x + 3) = 3(x + 8)

4x + 12 = 3x + 24

x = 12

Substitute x = 12 in (1).

fraction = 12/(12 + 5)

= 12/17

So, the required fraction is 12/17.

14. Answer :

Let b be the number of boys and g be the number of girls in the school.

From the given information,

b + g = 501 ----(1)

b = 2g + 3 ----(2)

We can solve the above system of linear equations in two variables using substitution method.

Substitute b = 2g + 3 in (1).

2g + 3 + g = 501

3g + 3 = 501

Subtract 3 from both sides.

3g = 498

Divide both sides by 3.

g = 166

Substitute g = 166 in (2).

b = 2(166) + 3

b = 332 + 3

b = 335

Therefore,

number of boys = 335

number of girls = 166

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