35.7k views
4 votes
Solve the system of equations algebraically.

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

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

User Irmak
by
8.5k points

2 Answers

2 votes

Answer:

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)

User JasonWoof
by
7.4k points
5 votes

Answer:

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.

User HighFlyingSmurfs
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories