Question

Which system of equations has exactly one solution?

A.) 2 x minus 4 y = 8. x + y = 7.
B.) 3 x + y = negative 1. 6 x + 2 y = negative 2.
C.) 3 x + 3 y = 3. Negative 6 x minus 6 y = 3.
D.) 3 x minus 2 y = 4. Negative 3 x + 2 y = 4.

Answer 1

A.) 2 x minus 4 y = 8. x + y = 7.

Explanation:

A.) 2 x minus 4 y = 8. x + y = 7.

2x - 4y = 8

x - 2y = 4

x = 4 + 2y

x + y = 7

4 + 2y + y = 7

3y = 3

y = 1

x = 4 + 2

x = 6

Only solution: (6,1)

Answer 2

A.) 2 x minus 4 y = 8. x + y = 7.

Explanation:

A.) 2 x minus 4 y = 8. x + y = 7.

2x-4y = 8

x+y=7

This has one solution

B.) 3 x + y = negative 1. 6 x + 2 y = negative 2.

3x+y = -1

Multiply by 2

6x +2y = -2

This is the second equation so it has infinite solutions

C.) 3 x + 3 y = 3. Negative 6 x minus 6 y = 3.

3x+3y =3

Multiply by -2

-6x-6y = -6

The equation is the same but the constant, which means they are parallel lines, they have zero solutions

D.) 3 x minus 2 y = 4. Negative 3 x + 2 y = 4.

3x -2y = 4

Multiply by -1

-3x +2y = -4

The equation is the same but the constant, which means they are parallel lines, they have zero solutions