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Introduction To Euclid's Geometry

Question
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Write four solutions for each of the following equations:

2x + y = 7

Solution

2x +y = 7
2x + y = 7
⇒ y = 7 – 2x
Put x = 0, we get y = 7 – 2(0) = 7 – 0 = 7
Put x = 1, we gety = 7 – 2(1) = 7 – 2 = 5
Put x = 2, we get y = 7 — 2(2) = 7 – 4 = 3
Put x = 3, we get y = 7 – 2(3) = 7– 6 = 1
∴ Four solutions are (0, 7), (1, 5), (2, 3) and (3, 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.

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