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Linear Equations in Two Variables

Short Answer Type

21. Check which of the following are solutions of the equation x – 2y = 4 and which are not:
(2, 0)

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22. Check which of the following are solutions of the equation x – 2y = 4 and which are not:
(4, 0)

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23. Check which of the following are solutions of the equation x – 2y = 4 and which are not:

open parentheses square root of 2 comma space 4 square root of 2 close parentheses

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24. Check which of the following are solutions of the equation x – 2y = 4 and which are not:

(1, 1)

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25. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.

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26.

Find at least 3 solutions for the following linear equation in two variables:

2x + 5y = 13

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27.
Find solutions of the form x = a, y = 0 and x = 0, y = b for the following pairs of equations. Do they have any common such solution?

3x + 2y = 6 and 5x + 2y = 10

3x + 2y = 6
Put y = 0, we get 3x + 2(0) = 6
$rightwards double arrow$ 3x = 6

$rightwards double arrow$ $straight x equals 6 over 3 equals 2$
$therefore space space space space space space space$ (0, 3) is a solution

5x + 2y = 10
Put y = 0, we get 5x + 2(0) = 10

$rightwards double arrow$ 5x = 10

$rightwards double arrow$ $straight y space equals 10 over 2 equals 5$
$therefore$ (0, 5) is a solution.

The given equations have a common solution (2, 0)