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) x – y/5 – 10 = 0. (ii) -2x+3y = 6. (iii) y – 2 = 0
Answers
( 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\:=\:0x−5y-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
Step-by-step explanation:
first part x minus y by 5 minus 10 is equal to zero
second part - 2 x + 3 y - 6 is equal to zero third part x plus y minus 2 is equal zero
now the values of a b and c in each
now first part a is equal to 1 1B is equal to minus 1 by 5 and c is equal to minus 10.
second second parts a is equal to minus 2 is equal to plus 3 c is equal to minus 6.
third part a is equal to zero b is equal to plus one and c is equal to minus.
hope you are satisfied with my answer