Question

Which statement describes the system of equations?

Answer 1

Answer:

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

Step-by-step 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 , $\frac{a1}{a2} = \frac{1}{1}, \frac{b1}{b2} =\frac{2}{-2} = -1 , \frac{c1}{c2} = \frac{2}{-2} =-1$

Here, $\frac{a1}{a2} \neq \frac{b1}{b2}$

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).

Step-by-step 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)