Question

Which statement describes the system of equations?

x+2y=2
x-2y=-2
It has infinitely many solutions.
It has no solution.
It has one solution (0, 1).
It has one solution (4, -1).

Answer 1

Option 3 - It has one solution (0, 1).

Explanation:

Given : The system of equations,

Equation 1 -
`x+2y=2`

Equation 2 -
`x-2y=-2`

To find : Which statement describes the system of equations?

Solution :

We solve equation 1 and 2,

Add equation 1 and 2,

`x+2y+x-2y=2-2`

`2x=0`

`x=0`

Substitute in equation 1,

`0+2y=2`

`y=(2)/(2)`

`y=1`

The solution of the equations is (0,1).

So, It has one solution (0, 1).

Therefore, Option 3 is correct.

Answer 2

it has one solution (0,1)

Explanation:

1)eliminate y

x + 2y + x -2y = 0

2x = 0 x = 0

2)eliminate x

x + 2y - x + 2y = 4

4y = 4

y = 1