Question

2x + 6y = 21 and -2x + 3y = 24

Answer 1

`x = -(9)/(2) , y = 5`

Explanation:

1. Solve 2x + 6y = 21 for x.

Step 1: Add -6y to both sides

• 
  `2x + 6y - 6y = 21 -6y`
• 
  `2x = -6y + 21`

Step 2: Divide both sides by 2.

• 
  `(2x)/(2) = (-6y+21)/(2)`

• 
  `x = -3y + (21)/(2)`

2. Substitute -3y + 21/2 for x in -2x + 3y = 24.

Step 1: Simplify both sides of the equation.

• 
  `-2(-3y+(21)/(2)) + 3y = 24`
• 
  `9y - 21 = 24`

Step 2: Add 21 to both sides.

• 
  `9y - 21 + 21 = 24 + 21`
• 
  `9y = 45`

Step 3: Divide both sides by 9.

• 
  `(9y)/(9) = (45)/(0)`
• 
  `y = 5`

3. Substitute 5 for y in x = -3y + 21/2

Step 1: Simplify both sides of the equation.

• 
  `x = -3y + (21)/(2)`
• 
  `x = -3(5) + (21)/(2)`
• 
  `x = -15 + (21)/(2)`
• 
  `x = -(9)/(2)`

Therefore, x = -9/2 and y = 5.