Question

Which variable will you choose to eliminate? How? -3x -8y=-24 and 3x - 5y= 45

Answer 1

Answer:

I'll choose 'x' variable first to eliminate because -

• -3 (coefficient of 'x' in Eqn.1)  & 3 (coefficient of 'x' in Eqn.2) are additive inverses of each other , so they can be easily eliminated by simply adding those equations.
• It can be also solved by using elimination method but you'll need to multiply -1 with either Eqn.1 or Eqn.2 because in elimination method , a variable can be eliminated only when their coefficients are numerically equal (along with their sign).

Step-by-step explanation:

Eqn.1 → -3x - 8y = -24

Eqn.2 → 3x - 5y = 45

If we'll add both the equations , then '3x' would be getting cancelled first.

⇒ $(-3x - 8y) + (3x - 5y) = (-24) + (45)$

⇒ $3x - 3x - 8y - 5y = 45 - 24$

⇒ $-13y = 21$

⇒ $y = \frac{-21}{13}$

Putting the value of y in eqn.2 ,

⇒ $3x - 5(\frac{-21}{13}) = 45$

⇒ $3x + \frac{105}{13} = 45$

⇒ $3x = 45 - \frac{105}{13}$

⇒ $3x = \frac{585 - 105}{13} = \frac{480}{13}$

⇒ $x = \frac{480}{13 \times 3} = \frac{480}{39}$

Reducing the fraction gives ,

⇒ $x = \frac{160}{13}$

Answer 2

Answer:

Lets choose y

• -8y=3x-24
• y=-3/8x+3

Plug in

• 3x+15/8x-15=45
• 39/8x= 60
• x=480/39