Exercise 4.1 Practice
Introduction to Linear Equations in Two Variables
Q1: Form Equation
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The cost of a shirt is three times the cost of a tie. Write a linear equation in two variables to represent this statement.
(Take the cost of a shirt to be $₹ x$ and that of a tie to be $₹ y$).
(Take the cost of a shirt to be $₹ x$ and that of a tie to be $₹ y$).
Let the cost of a shirt be $x$ and the cost of a tie be $y$.
According to the statement: Cost of shirt = $3 \times$ Cost of tie.
So, $x = 3y$.
Rearranging to standard form: $x - 3y = 0$.
$x - 3y = 0$
Q2: Standard Form
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Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in each case:
(i) $3x + 5y = 7.2$
(ii) $x - \frac{y}{4} - 8 = 0$
(iii) $-3x + 2y = 9$
(iv) $x = 5y$
(v) $4x = -3y$
(vi) $5x + 4 = 0$
(vii) $y - 3 = 0$
(viii) $8 = 2x$
(i) $3x + 5y = 7.2$
(ii) $x - \frac{y}{4} - 8 = 0$
(iii) $-3x + 2y = 9$
(iv) $x = 5y$
(v) $4x = -3y$
(vi) $5x + 4 = 0$
(vii) $y - 3 = 0$
(viii) $8 = 2x$
(i) $3x + 5y - 7.2 = 0$:
$a = 3, b = 5, c = -7.2$.
$a = 3, b = 5, c = -7.2$.
(ii) $1x - \frac{1}{4}y - 8 = 0$:
$a = 1, b = -1/4, c = -8$.
$a = 1, b = -1/4, c = -8$.
(iii) $-3x + 2y - 9 = 0$:
$a = -3, b = 2, c = -9$.
$a = -3, b = 2, c = -9$.
(iv) $x - 5y + 0 = 0$:
$a = 1, b = -5, c = 0$.
$a = 1, b = -5, c = 0$.
(v) $4x + 3y + 0 = 0$:
$a = 4, b = 3, c = 0$.
$a = 4, b = 3, c = 0$.
(vi) $5x + 0y + 4 = 0$:
$a = 5, b = 0, c = 4$.
$a = 5, b = 0, c = 4$.
(vii) $0x + 1y - 3 = 0$:
$a = 0, b = 1, c = -3$.
$a = 0, b = 1, c = -3$.
(viii) $2x + 0y - 8 = 0$:
$a = 2, b = 0, c = -8$.
$a = 2, b = 0, c = -8$.