Question

Which system has (-2, -2) as the solution?

Which system has no solutions?
Which system has infinite solutions?


A. x + y = -1
4x + 4y = -4
B. x + y = -4
-3x + 2y = 2
C. 4x + 6y = -12
2x + 3y = 9
D. x - y = -2
3x - y = 0
E. x - 4y = -8
2x - 3y = -16

Answer 1

The answer is B. Plug -2 in for x and y to see which equations are true

Answer 2

Q1. The answer is
B. x + y = -4
-3x + 2y = 2

Let's substitute x and y in all of the choices:
A. x + y = -1
-2 -2 = -1
-4 = -1 INCORRECT
B x + y = -4
-2 -2 = -4 CORRECT
So, the answer is B.

Q3. The answer is
A. x + y = -1
4x + 4y = -4

Let's solve all choices except B (because we know its solution).
A. x + y = -1
4x + 4y = -4
_______
x = - 1 - y
4x + 4y = -4
______
4(-1-y) + 4y = -4
-4 - 4y + 4y = -4
0 = -4 + 4
0 = 0
This system has infinite solutions.


Q2. The answer is
C. 4x + 6y = -12
2x + 3y = 9

4x + 6y = -12
2x + 3y = 9
_________
4x + 6y = -12
-2(2x + 3y) = -2 * 9
_________
4x + 6y = -12
-4x - 6y = -18
_________
4x - 4x + 6y - 6y = -12 + -18
0 + 0 = -30
This system has no solutions.