Elimination Add or Subtract

Solve the system by elimination.
−8x − 10y = 20
−8x − 6y = −4

• Infinite number of solutions  

• (6, 5) 

• (−6, −5) 

• (5, −6) 

Solve by elimination

-6x + 5y = 1

6x + 4y = -10

• (-1,7/5)

• (0,-1)

• (1,1)

• (-1,-1)

Solve by elimination:
-9x - 4y = -20
5x + 4y = 4

• (-4,4)

• (4,4)

• (4,-4)

• (-4,-4)

Solve by elimination:

7x + y = -9

-3x - y = 5

• No solution

• (1,8)

• (-1,-3)

• (-1,-2)

How do you know if you should ADD or SUBTRACT the two equations?

Consider the system of equations:

6x-10y=2

6x+2y=24

Should we add or subtract to eliminate a variable?

• ADD, because the 6s have the same sign

• SUBTRACT, because the 6s have the same sign

• ADD, because the 6s have OPPOSITE signs

• SUBTRACT, because the 6s have opposite signs

Consider the system of equations: 2x+4y=10 12x-4y=20 Should we add or subtract to eliminate a variable?

• ADD, because the 4s have the same sign

• SUBTRACT, because the 4s have the same sign

• ADD, because the 4s have OPPOSITE signs

• SUBTRACT, because the 4s have opposite signs

Consider the system of equations:

12x+6y=-54

12x-6y=18

Should we add or subtract to eliminate a variable?

• ADD, because the 12s have the same sign

• SUBTRACT, because the 12s have the same sign

• ADD, because the 6s have OPPOSITE signs

• SUBTRACT, because the 6s have opposite signs

How do we know if we need to ADD or SUBTRACT in order to eliminate a variable?

Consider the system: 4x+6y=14 4x-2y=10 Should we ADD or SUBTRACT to eliminate a variable?

• SUBTRACT, because the 4s have the same sign

• ADD, because the 4s have the same sign

• SUBTRACT, because the 4s have oppostie signs

• ADD, because the 4s have opposite signs

Answer explanation

Once you find coefficients that are the same, check their signs.

If the same sign, subtract equations

If opposite signs, add the equations