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

-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.

Answer 2

The correct answer is option d. (1,0)

Explanation:

It is given that,

4x-2y=4

6x-4y=6

We can solve the system of equations algebraically

To solve the equations

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

⇒ 2x - y = 2 -----(2)

6x-4y=6 ------(3)

⇒ 3x - 2y = 3 -----(4)

eq(2) * 2 ⇒ 4x - 2y = 4 ----(5)

eq(5) - eq(4) ⇒

4x - 2y = 4

3x - 2y = 3

-------------------

x + 0 = 1

Substitute the value of x in eq (1)

(4*1) - 2y = 4

4 - 2y = 4

2y= 0

y = 0

Therefore the solution of this system of equations is (1,0)

The correct answer is option d. (1,0)