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

(0,1) is the unique solution of the system .

Explanation:

The given sets of equations are

x + 2y = 2

x - 2y = -2

Compare the equations with ax + by = c

Here, we get a1 = 1, b1 = 2 and c1 = 2

and a2 = 1, b2 = -2 and c2 = -2

Now, as we can see ,
`(a1)/(a2)  = (1)/(1),  (b1)/(b2) =(2)/(-2) = -1 ,  (c1)/(c2)   = (2)/(-2) =-1`

Here,
`(a1)/(a2)  \\eq  (b1)/(b2)`

Hence, the system has UNIQUE SOLUTION.

And, (0,1) is the unique solution of the system

x + 2y = 0 + 2(1) = 2 = Right side

and x - 2y = 0 - 2(1) = -2 = Right side

Answer 2

Answer: It has one solution (0, 1).

Explanation:

x+2y=2

x-2y=-2

This equation can be solve by either substitution method or by elimination method or both method

We shall use the two method to solve this equations

x+2y=2 ----------------(1)

x-2y=-2-----------------(2)

To eliminate x, I will simply subtract equation (2) from equation (1)

(x-x=0 2y -[-2y] = 4y 2-[-2]=4)

The equation becomes;

4y = 4

So to get the value of y, we will simply divide both-side of the equation by 4

4y/4 = 4/4

y = 1

substitute y=1 to any of the equation, either equation (1) or equation (2)

Lets substitute y=1 in equation (1)

x+2y=2

x + 2(1) =2

x + 2 = 2

To get the value of x, we will simply subtract 2 from both-side

x + 2 - 2 = 2-2

x = 0

Therefore the solution of these equations is;

x=0 and y=1

(0,1)

Hence, the system of equations has one solution which is (0, 1)