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Question 5:

A pair of linear equations which has a unique solution $x = 2, y = -3$ is:

We test each option by substituting $x = 2$ and $y = -3$ into both equations:

• Option a:

  • $x + y = -1 \implies 2 - 3 = -1$ (True)
  • $2x - 3y = -5 \implies 2(2) - 3(-3) = 4 + 9 = 13$ (False)

• Option b:

  • $2x + 5y = -11 \implies 2(2) + 5(-3) = 4 - 15 = -11$ (True)
  • $4x + 10y = -22 \implies 4(2) + 10(-3) = 8 - 30 = -22$ (True)

• Option c:

  • $2x - y = 1 \implies 2(2) - (-3) = 4 + 3 = 7$ (False)

• Option d:

  • $x - 5y - 14 = 0 \implies 2 - 5(-3) - 14 = 2 + 15 - 14 = 3$ (False)

Answer: The correct option is b.

Question 6:

Which of the following is a valid solution to the equation $3(x + 4) = 2(x - 1)$?

Simplify the equation: $3x + 12 = 2x - 2$ $3x - 2x = -2 - 12$ $x = -14$

The correct solution is $x = -14$.

Answer: The correct option is c.

Question 7:

Solve the following system of linear equations: $x + y = 7 \quad \text{(1)}$ $2x - 3y = 4 \quad \text{(2)}$

From (1), express $y$ in terms of $x$: $y = 7 - x$

Substitute into (2): $2x - 3(7 - x) = 4$ $2x - 21 + 3x = 4$ $5x = 25 \implies x = 5$

Substitute $x = 5$ into (1): $5 + y = 7 \implies y = 2$

Now calculate $3x - 2y$: $3(5) - 2(2) = 15 - 4 = 11$

Answer: The correct option is d (11).

Question 8:

Consider the data set $5, 6, 7, 7, 7, 8, 9$. What is the median?

1. Arrange the data in order (already done): $5, 6, 7, 7, 7, 8, 9$.
2. Since there are 7 numbers (odd count), the median is the middle value:
   • The 4th value is $7$.

Answer: The correct option is b (7).

Question 9:

The graph of the point $(-4, 0)$ will lie on:

The point $(-4, 0)$ has a $y$-coordinate of $0$, meaning it lies on the X-axis.

Answer: The correct option is a (X-axis).

Question 10:

The factors of the quadratic expression $x^2 + 7x + 10$ are:

Factorize: $x^2 + 7x + 10 = (x + 5)(x + 2)$

Answer: The correct option is a (x + 2)(x + 5).

Summary of Answers:

1. Question 5: b
2. Question 6: c
3. Question 7: d
4. Question 8: b
5. Question 9: a
6. Question 10: a

Do you want detailed explanations for any of these questions? Let me know!

Here are 5 related questions to practice:

1. Solve the system: $3x + y = 8$ and $x - 2y = 3$.
2. Find the median of $12, 15, 11, 14, 10, 13$.
3. Solve $5(x + 1) = 3(x - 4)$.
4. Factorize $x^2 + 9x + 20$.
5. Which quadrant does the point $(-3, 5)$ lie in?

Tip: Always substitute solutions back into equations to verify accuracy!