Solve the system of equations algebraically.
4x-2y=8
2x-4y=4

a. (1,1) b. no solution
c.(2,0) d. many solutions

The correct option is c.

Step-by-step explanation:

The given equations are

       ....(1)

       ....(2)

Multiply equation (1) by 2 and multiply equation (2) by 4.

       ....(3)

       ....(4)

Subtract equation (4) from equation (3).

Put this value in equation (1).

The solution of the system of equations is (2,0).

Therefore option c is correct.

Option c. (2,0)

Step-by-step explanation:

(1) 4x-2y=8

(2) 2x-4y=4

Using the method of elimination: Multiplying the second equation by -2:

(2)   -2(2x-4y)=-2(4)

Applying the distributive property:

-2(2x)-2(-4y)=-8

-4x+8y=-8

Adding this equation with the first equation:

-4x+8y+4x-2y=-8+8

6y=0

Solving for "y": Dividing both sides of the equation by 6:

6y/y=0/6

y=0

Replacing y=0 in the second equation:

(2) 2x-4(0)=4

2x-0=4

2x=4

Solving for "x": Dividing both sides of the equation by 2:

2x/2=4/2

x=2

The solution is (x,y)=(2,0)

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