Question

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) 2x + 3y = 9.35
(ii) x-y/5-10= 0
(iii) – 2x + 3y = 6
(iv) x = 3y
(v) 2x = -5y
(vi) 3x + 2 = 0
(vii) y – 2 = 0
(viii) 5 = 2x

Answer 1

$\huge\bf\underline{Solution:-}$

we need to express the given Linear equations in the form of ax + by + c = 0 and also indicate the value of a , b and c.

Case(i)

• (i) 2x+3y = 9.35

expressing in the form of ax + by + c = 0

2x + 3y - 9.35 = 0

where

• a = 2
• b = 3
• c = -9.35

Case (ii)

• (ii) x-y/5-10= 0

$\mapsto \rm \: \frac{x - y}{5} - 10 = 0 \\ \\ \mapsto \rm \: \frac{x - y - 50}{5} = 0 \\ \\ \mapsto \rm \: x - y - 50 = 0 \times 5$

expressing in the form of ax + by + c = 0

x - y -50 = 0

where

• a = 1
• b = -1
• c = -50

Case (iii)

• (iii) – 2x + 3y = 6

expressing in the form of ax + by + c = 0

$\rm \mapsto \:2x - 3y + 6 = 0$

where ,

• a = 2
• b = -3
• c = 6

Case (iv)

• (iv) x = 3y

expressing in the form of ax + by + c = 0

$\mapsto \rm \:x - 3y + 0= 0$

where

• a = 1
• b = -3
• c = 0

Case (v)

• (v) 2x = -5y

expressing in the form of ax + by + c = 0

$\rm \mapsto \: 2x + 5y + 0 = 0$

• a = 2
• b = 5
• c = 0

Case (vi)

• (vi) 3x + 2 = 0

expressing in the form of ax + by + c = 0

$\rm \mapsto \: 3x + 0y + 2 = 0$

where,

• a = 3
• b = 0
• c = 2

Case (vii)

• (vii) y-2 = 0

expressing in the form of ax + by + c = 0

$\rm \mapsto \: 0x + y - 2 = 0$

where,

• a = 0
• b = 1
• c = -2

Case (viii)

• (viii) 5 = 2x

expressing in the form of ax + by + c = 0

$\rm \mapsto \: 5 = 2x \\ \\ \rm \mapsto \: 5 - 2x = 0 \\ \\ \rm \mapsto \: 2x + 0y - 5 = 0$

where,

• a = 2
• b = 0
• c = -5

Answer 2

Answer:

( i ) 2x + 3y - 9.35 = 0

( ii ) 5x - y - 50 = 0

( iii ) - 2x + 3y - 6 = 0

( iv ) x - 3y + 0 = 0

( v ) 2x + 5y + 0 = 0

( vi ) 3x + 0y + 2 = 0

( vii ) 0x + y - 2 = 0

( viii ) - 2x + 0y + 5 = 0

Step-by-step-explanation:

We have given some linear equations in two variables.

We have to express them in the general form

ax + by + c = 0 and indicate the values of a, b and c.

( i ) 2x + 3y = 9.35

➞ 2x + 3y - 9.35 = 0

Comparing with ax + by + c = 0, we get,

• a = 2
• b = 3
• c = - 9.35

( ii ) $\sf\:x\:-\:\frac{y}{5}\:-\:10\:=\:0$

Multiplying each term by 5, we get,

➞ 5x - y - 50 = 0

Comparing with ax + by + c = 0, we get,

• a = 5
• b = - 1
• c = - 50

( iii ) - 2x + 3y = 6

➞ - 2x + 3y - 6 = 0

Comparing with ax + by + c = 0, we get,

• a = - 2
• b = 3
• c = - 6

( iv ) x = 3y

➞ x - 3y + 0 = 0

Comparing with ax + by + c = 0, we get,

• a = 1
• b = - 3
• c = 0

( v ) 2x = - 5y

➞ 2x + 5y = 0

➞ 2x + 5y + 0 = 0

Comparing with ax + by + c = 0, we get,

• a = 2
• b = 5
• c = 0

( vi ) 3x + 2 = 0

➞ 3x + 0y + 2 = 0

Comparing with ax + by + c = 0, we get,

• a = 3
• b = 0
• c = 2

( vii ) y - 2 = 0

➞ 0x + y - 2 = 0

Comparing with ax + by + c = 0, we get,

• a = 0
• b = 1
• c = - 2

( viii ) 5 = 2x

➞ 5 - 2x = 0

➞ - 2x + 5 = 0

➞ - 2x + 0y + 5 = 0

Comparing with ax + by + c = 0, we get,

• a = - 2
• b = 0
• c = 5

Additional Information:

1. Linear Equations in two variables:

The equation with the highest index

( degree ) 1 is called as linear equation. If the equation has two different variables, it is called as 'linear equation in two variables'.

The general formula of linear equation in two variables is

ax + by + c = 0

Where, a, b, c are real numbers and

a ≠ 0, b ≠ 0.

2. Solution of a Linear Equation:

The value of the given variable in the given linear equation is called the solution of the linear equation.