Question

Solve the system and determine the best method to solve each system of equations

Answer 1

Best Method: Elimination

x = -2

y = 2

Explanation:

Hello!

We can solve the system by elimination.

To solve by elimination, we want to completely eliminate a variable. To do that, we need to have that variable in the equations with the same or opposite coefficients. Then we can subtract or add them accordingly.

Solve for x

• 
  `\left \{ {{3x + 7y = 8} \atop {6x + 7y = 2}} \right.`
• 
  `-\left \{ {{3x + 7y = 8} \atop {6x + 7y = 2}} \right.` Vertically subtract them
• 
  `(3x - 6x) + (7y - 7y) = (8 - 2)`
• 
  `-3x = 6`
• 
  `x = -2`

Solve for y

Plug -2 for x into any equation for y

• 
  `3x + 7y = 8`
• 
  `3(-2) + 7y = 8`
• 
  `-6 + 7y = 8`
• 
  `7y = 14`
• 
  `y = 2`

The solution to the system: (-2,2)

x = -2

y = 2