Linear Equations

13 Grade 8 Mathematics questions on Linear Equations, with worked marking schemes. 13 questions are available on this topic in full.

1. Question 1

   3 marks

   Solve the simultaneous equations: $x+y=12$ and $2x-y=6$.

   (3 marks)

   Marking scheme

   The $y$ terms are $+y$ and $-y$, so adding the two equations eliminates $y$. (1)

   $(x+y)+(2x-y)=12+6$ gives $3x=18$, so $x=6$. (1)

   Substitute $x=6$ into the first equation: $6+y=12$, so $y=6$. (1)

   Final answer: $x=6$, $y=6$. Check in the second: $2(6)-6=6$.

2. Question 2

   1 mark

   Solve: $3x-7=11$

   A. 4

   B. 6

   C. 18

   D. 3

   (1 mark)

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3. Question 3

   1 mark

   The sum of a number and 8 is 21. Find the number.

   A. 29

   B. 8

   C. 21

   D. 13

   (1 mark)

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4. Question 4

   1 mark

   Given $2x+y=11$ and $x=y+1$, find x.

   A. 4

   B. 3

   C. 5

   D. 7

   (1 mark)

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5. Question 5

   1 mark

   Given $x+y=10$ and $x-y=4$, find the value of x.

   A. 7

   B. 3

   C. 14

   D. 6

   (1 mark)

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6. Question 6

   4 marks

   3 pens and 2 books cost Ksh 210. 1 pen and 1 book cost Ksh 80. Find the cost of a pen and the cost of a book.

   (4 marks)

   Marking scheme

   Let pen = x, book = y. From x + y = 80, y = 80 - x.

   3x + 2(80 - x) = 210 → x + 160 = 210 → x = 50.

   y = 80 - 50 = 30. Pen = Ksh 50, book = Ksh 30.

7. Question 7

   4 marks

   The length of a rectangle is 3 cm more than its width. Its perimeter is 26 cm. Find the width.

   (4 marks)

   Marking scheme

   Let the width be $w$ cm. The length is $3$ cm more, so it is $w+3$. (1)

   The perimeter of a rectangle is $2(\text{length}+\text{width})$, so $2(w+3+w)=26$. (1)

   Expand: $4w+6=26$, so $4w=20$. (1)

   Divide by $4$: $w=5$. Check: length $8$ cm, perimeter $2(8+5)=26$ cm. (1)

   Final answer: the width is $5$ cm.

8. Question 8

   1 mark

   Solve: $2x+7=3x-4$

   A. 3

   B. 11

   C. 1

   D. -11

   (1 mark)

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9. Question 9

   1 mark

   Solve: $\frac{x}{3}+2=6$

   A. 24

   B. 2

   C. 12

   D. 8

   (1 mark)

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10. Question 10

    1 mark

    Solve: $3(x-2)=9$

    A. 1

    B. 11

    C. 5

    D. 3

    (1 mark)

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11. Question 11

    1 mark

    Solve: $5x=35$

    A. 30

    B. 40

    C. 175

    D. 7

    (1 mark)

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12. Question 12

    1 mark

    Solve: $4x-3=17$

    A. 3.5

    B. 20

    C. 14

    D. 5

    (1 mark)

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13. Question 13

    1 mark

    Given $2x+3y=12$ and x = 3, find y.

    A. 3

    B. 2

    C. 6

    D. 1

    (1 mark)

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