Question

express x in terms of y

a) ( x + 3y = 0 )

b) ( x - 2y = 0 )

c) ( x + y - 5 = 0 )

i) ( 2x + y - 4 = 0 )
ii) ( 3x + y + 5 = 0 )
iii) ( 4x = 3y )

Explanation:

To solve for \( x \) in terms of \( y \) for each equation, we'll isolate \( x \) by performing algebraic operations.

Part (a): \( x + 3y = 6 \)

Step 1: Subtract \( 3y \) from both sides

To isolate \( x \), we subtract \( 3y \) from both sides of the equation:
\( x + 3y - 3y = 6 - 3y \)

Step 2: Simplify

Simplifying the left side ( \( 3y - 3y = 0 \) ) gives:
\( x = 6 - 3y \)

Part (b): \( x - 2y = 6 \)

Step 1: Add \( 2y \) to both sides

To isolate \( x \), we add \( 2y \) to both sides of the equation:
\( x - 2y + 2y = 6 + 2y \)

Step 2: Simplify

Simplifying the left side ( \( -2y + 2y = 0 \) ) gives:
\( x = 6 + 2y \)

Part (c): \( x + y - 5 = 0 \)

Step 1: Add 5 and subtract \( y \) from both sides

To isolate \( x \), we add 5 to both sides and subtract \( y \) from both sides:
\( x + y - 5 + 5 - y = 0 + 5 - y \)

Step 2: Simplify

Simplifying the left side ( \( y - y = 0 \) and \( -5 + 5 = 0 \) ) gives:
\( x = 5 - y \)

Final Answers:

• (a) \( \boldsymbol{x = 6 - 3y} \)
• (b) \( \boldsymbol{x = 6 + 2y} \)
• (c) \( \boldsymbol{x = 5 - y} \)

Answer:

To solve for \( x \) in terms of \( y \) for each equation, we'll isolate \( x \) by performing algebraic operations.

Part (a): \( x + 3y = 6 \)

Step 1: Subtract \( 3y \) from both sides

To isolate \( x \), we subtract \( 3y \) from both sides of the equation:
\( x + 3y - 3y = 6 - 3y \)

Step 2: Simplify

Simplifying the left side ( \( 3y - 3y = 0 \) ) gives:
\( x = 6 - 3y \)

Part (b): \( x - 2y = 6 \)

Step 1: Add \( 2y \) to both sides

To isolate \( x \), we add \( 2y \) to both sides of the equation:
\( x - 2y + 2y = 6 + 2y \)

Step 2: Simplify

Simplifying the left side ( \( -2y + 2y = 0 \) ) gives:
\( x = 6 + 2y \)

Part (c): \( x + y - 5 = 0 \)

Step 1: Add 5 and subtract \( y \) from both sides

To isolate \( x \), we add 5 to both sides and subtract \( y \) from both sides:
\( x + y - 5 + 5 - y = 0 + 5 - y \)

Step 2: Simplify

Simplifying the left side ( \( y - y = 0 \) and \( -5 + 5 = 0 \) ) gives:
\( x = 5 - y \)

Final Answers:

• (a) \( \boldsymbol{x = 6 - 3y} \)
• (b) \( \boldsymbol{x = 6 + 2y} \)
• (c) \( \boldsymbol{x = 5 - y} \)