Question

Solve the system of equations algebraically.

4x-2y=4
6x-4y=6

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

Answer 1

Choice d is correct answer.

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).

Answer 2

Option (d) is correct.

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

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.