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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

2x + 5y = 13

$rightwards double arrow$ 5y = 13 - 2x

$rightwards double arrow$ $straight y equals fraction numerator 13 minus 2 straight x over denominator 5 end fraction$
Put x = 0, then $straight y equals fraction numerator 13 minus 2 left parenthesis 0 right parenthesis over denominator 5 end fraction equals 13 over 5$

Put x = 1, then $y equals fraction numerator 13 minus 2 left parenthesis 1 right parenthesis over denominator 5 end fraction equals 11 over 5$

Put x = 2, then $straight y equals fraction numerator 13 minus 2 left parenthesis 2 right parenthesis over denominator 5 end fraction equals 9 over 5$

Put x = 3, then $straight y equals fraction numerator 13 minus 2 left parenthesis 3 right parenthesis over denominator 5 end fraction equals 7 over 5$

$therefore space space space open parentheses 0 comma space 13 over 5 close parentheses comma space open parentheses 1 comma space 11 over 5 close parentheses comma space open parentheses 2 comma space 9 over 5 close parentheses space a n d space space open parentheses 3 comma space 7 over 5 close parentheses$ are the solutions of equation 2x + 5y = 13.