Question

1.1. Which statement explains why the two systems of equations below have the

same solution?
A(6x + 8y = -10
2x - 5y = 12
B
8x + 3y = 2
12x + 16y = - 20
A. The first equation in B is the sum of the equations in A, while the other is obtained
by multiplying the second equation in A by 6.
B. The first equation in B is the sum of the equations in A, while the other is obtained
by multiplying the first equation in A by 2.
C. The equations in A are increased by 12 and -32 to get the equations in
D. The equations in A are multiplied by 2 and 4 to get the equations in B.

Answer 1

Correct Answer is B. The first equation in B is the sum of the equations in A, while the other is obtained by multiplying the first equation in A by 2.

Explanation:

As given,

A : 6x + 8y = -10 .......equation (1)

2x - 5y = 12 .......equation (2)

B : 8x + 3y = 2 .......equation (1)

12x + 16y = - 20 .......equation (1)

Correct Answer is B. The first equation in B is the sum of the equations in A, while the other is obtained by multiplying the first equation in A by 2.

Proof :

The first part says that ,

Sum of equation (1) of A and equation (2) of A = Equation (1) of B

Firstly , find the Sum of equation (1) of A and equation (2) of A

⇒6x + 8y + 2x - 5y = -10 + 12

⇒8x + 3y = 2

this is same as equation (1) of B

So, it satisfies the first part

The second part says that,

The equation (2) of B is obtained by multiplying the first equation in A by 2.

It means , if the equation (1) is multiplied by 2 = equation (2) of B

Firstly , if the equation (1) is multiplied by 2 , we get

2 ( 6x + 8y = -10 )

⇒ 2 ( 6x + 8y ) = 2 ( -10)

⇒ 12x + 16y = -20

this is same as equation (2) of B

So, it satisfies the second part.