Solve the system of equations algebraically.

4x-2y=4

6x-4y=6

a. no solution

b. many solutions

c. (0,1)

d. (1,0)

Choice d is correct answer.

Step-by-step explanation:

We have given a system of equations.

4x-2y = 4 eq (1)

6x-4y = 6 eq (2)

We have to solve it for x and y.

We use method of elimination to solve this system.

Multiplying by 2 to both sides of eq (1), we have

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

8x-4y = 8 eq (3)

Subtracting eq (3) to eq (2), we have

8x-4y - (6x-4y) = 8-6

8x-4y-6x+4y = 2

2x = 2

Dividing by 2 to both sides of qbove equation, we have

2x/2 = 2/2

x = 1

Putting the value of x in eq (1), we have

4 (1) - 2y = 4

4-2y = 4

Adding - 4 to both sides of above equation, we have

-2y = 0

Dividing by - 2 to both sides of above equation, we have

y = 0

Hence, the solution of given system is (1,0).

Option (d) is correct.

(1, 0) is the solution of the given system of equation.

Step-by-step explanation:

Consider the given system of equation

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

6x - 4y = 6 ... (2)

We have to solve the system algebraically,

We will solve it by elimination method,

Multiply equation (1) by 2, we get,

(1) ⇒ 8x - 4y = 8 ... (3)

Subtract equation (2) from (3), we get,

8x - 4y - (6x - 4y) = 8 - 6

8x - 4y - 6x + 4y = 2

8x - 6x = 2

⇒ x = 1

Substitute x = 1 in (1) and solve for y, we get,

⇒ 4x - 2y = 4 ⇒ 4 (1) - 2y = 4 ⇒ 2y = 4 - 4 ⇒ 2y = 0 ⇒ y = 0

Thus, (1, 0) is the solution of the given system of equation.

Option (d) is correct.