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 – \(\frac{y}{5}\)– 10 = 0 

(iii) –2x + 3y = 6 

(iv) x = 3y 

(v) 2x = –5y 

(vi) 3x + 2 = 0 

(vii) y – 2 = 0

Answer 1

(i) \( 2x + 3y = 9.35 \)

To express this in the form \( ax + by + c = 0 \), we subtract 9.35 from both sides: 
\( 2x + 3y - 9.35 = 0 \). 
Therefore, \( a = 2 \), \( b = 3 \), and \( c = -9.35 \).

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

To express this in the form \( ax + by + c = 0 \), we multiply through by 5 to eliminate the fraction: 
\( 5x - y - 50 = 0 \). 
Therefore, \( a = 5 \), \( b = -1 \), and \( c = -50 \).

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

To express this in the form \( ax + by + c = 0 \), we subtract 6 from both sides: 
\( -2x + 3y - 6 = 0 \). 
Therefore, \( a = -2 \), \( b = 3 \), and \( c = -6 \).

(iv) \( x = 3y \)

To express this in the form \( ax + by + c = 0 \), we subtract \( 3y \) from both sides: 
\( x - 3y = 0 \). 
Therefore, \( a = 1 \), \( b = -3 \), and \( c = 0 \).

(v) \( 2x = -5y \)

To express this in the form \( ax + by + c = 0 \), we add \( 5y \) to both sides: 
\( 2x + 5y = 0 \). 
Therefore, \( a = 2 \), \( b = 5 \), and \( c = 0 \).

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

To express this in the form \( ax + by + c = 0 \), we subtract 2 from both sides: 
\( 3x + 2 - 2 = 0 \), or \( 3x = -2 \). 
Therefore, \( a = 3 \), \( b = 0 \), and \( c = -2 \).

(vii) \( y - 2 = 0 \)

To express this in the form \( ax + by + c = 0 \), we add 2 to both sides: 
\( 0x + y - 2 = 0 \). 
Therefore, \( a = 0 \), \( b = 1 \), and \( c = -2 \).