Question

The solution to the system of equations shown is (2, 0).

3x − 2y = 6 
x + 4y = 2

When the first equation is multiplied by 2, the sum of the two equations is equivalent to 7x = 14
.

Which system of equations will also have a solution of (2, 0)?

6x - 4y = 6 
x + 4y = 2

6x − 4y = 6 
2x + 8y = 2

x + 4y = 2 
7x = 14

6x − 4y = 6 
7x = 14

Answer 1

Option C is correct.

Explanation:

We use the following result:

When the multiples of the equations in a system is added or subtracted, the resulting equation together with any of the original equation will result in the same answer.

Given equations,

3x − 2y = 6 ......(1)

x + 4y = 2 .............(2)

multiply eqn. (1) with 2 and add to (2) we get

2 × ( 3x − 2y ) + x + 4y = 2 × 6 + 2

7x = 14 ......(3)

So, by result and eqn (2) and (3)

we have the required system of equations

x + 4y = 2

7x = 14

which will also have a solution of (2, 0)

Therefore, Option C is correct.

Answer 2

Your choice should be

`x+4y=2\\7x=14`

This system consists of the second of the given equations and the one you developed that is their sum.