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Introduction To Euclid's Geometry

Question
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Express x = 3y in the form ax + by + c = 0 and indicate the values of a, b and c. Write two solutions of the equation.

Solution

                            x = 3y
rightwards double arrow     x - 3y = 0
rightwards double arrow   1(x) + (- 3)y + (0) = 0
Comparing with ax + by + c = 0, we get
                      a = 1
                      b = -3
                      c = 0
Now,               x = 3y
rightwards double arrow                  straight y space equals space straight x over 3
Put x = 0, then  y = 0 over 3 equals 0
Put x = 3, then  y = 3 over 3 equals space 1
Hence, (0,0) and (3,1) are the two solutions of the equation x = 3y.

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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