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Introduction To Euclid's Geometry

Question

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

Solution

(0, 2)
Put x = 0 and y = 2 in (i)., we get
x - 2y = 0 -2(2) = - 4, which is not 4
$therefore$ (0, 2) is not a solution of (1).

Some More Questions From Introduction to Euclid's Geometry Chapter

Express the following statement as a linear equation in two variables by taking present ages (in years) of father and son as x and y, respectively. Age of father 5 years ago was two years more than 7 times the age of his son at that time.

Write the equation 2x = y in the form ax + by + c = 0 and find the values of a, b, c in the equation. How many solution this equation has?

Express the linear equation 7 = 2x in the form ax + by + c = 0 and also write the values of a, b and c

Write each of the following as an equation in two variables:

(i) x = – 5 (ii) y = 2

(iii) 2x = 3 (iv) 5y = 2.

Which one of the following options is true, and why?

y = 3x + 5 has

(i) a unique solution,
(ii) only two solutions,
(iii) infinitely many solutions.

Write four solutions for each of the following equations:

2x + y = 7

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