Question

PLEASE HELP!!! 50 points!!!!!!

System A:
5x + 3y = 2
4x + 3y = 1
The system has no solution.
The system has a unique solution:
Equation:____________
The system has infinite solutions

System B:
y = 5x + 8
y = 5x + 5
The system has no solution.
The system has a unique solution:
Equation:____________
The system has infinite solutions

Answer 1

System A

The system has a unique solution: x=1, y=-1

System B

The system has no solution

Explanation:

System A

Use simultaneous equations to see if we can solve the system by multiplying the second equation by -1 and adding them together:

5x + 3y = 2

-4x - 3y = -1

We get (5-4)x+(3-3)y=(2-1), which simplifies to x=1

If x=1:

5+3y=2

3y=-3

y=-1

Since we have specific answers for x and y, we can say the system has a unique solution.

System B

If y is equal to both 5x+8 and 5x+5, that means

5x+8=5x+5

Subtracting 5x from both sides we get 8=5, which is illogical.

Therefore the system has no solution

Answer 2

System A: (1, -1)

System B: No solution