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Introduction To Euclid's Geometry

Question
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Write four solutions for each of the following equations:

πx plus straight y equals 9

Solution
πx plus straight y equals 9 rightwards double arrow space straight y space equals space 9 minus πx
Put x = 0, we get    y = 9 - straight pi(0) = 9 - 0 = 9
Put x = 1, we get    y = 9 -straight pi(1)= 9 - straight pi 
Put x =-1 we get    y = 9 -straight pi(-1 = 9 + straight pi

Put space straight x space equals space 9 over straight pi comma space we space get space straight y space equals space 9 space minus straight pi open parentheses 9 over straight pi close parentheses equals 9 minus 9 equals 0
therefore  Four solutions are (0, 9) (1, 9 - straight pi),
left parenthesis negative 1 comma space 9 plus straight pi right parenthesis space and space open parentheses 9 over straight pi comma space 0 close parentheses

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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