Question

Solve the system of equations algebraically.

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

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

Answer 1

Option c. (2,0)

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)

Answer 2

The correct option is c.

Explanation:

The given equations are

`4x-2y=8` ....(1)

`2x-4y=4` ....(2)

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

`8x-4y=16` ....(3)

`8x-16y=16` ....(4)

Subtract equation (4) from equation (3).

`8x-4y-8x+16y=16-16`

`12y=0`

`y=0`

Put this value in equation (1).

`4x-2(0)=8`

`4x=8`

`x=2`

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

Therefore option c is correct.